Chapter 8

Yes yoursquore taking notes didnrsquot I just give you an outline

Motion

What is motion

If I threw a ball from here to there can you tell me when the ball is in motion and when it isnt

Motion = ∆ location

bull In math ∆ means change in

bull What could affect the motion of the ball

ndashHow hard I throw the ballhellip I can change the speed

bull Change in speedndash Faster means it has to go the same distance in

a shorter timendash Slower means it has to go the same distance

in a longer timebull Think about when youre running to class

Gym - - - - - - - - - - - - - - - - - - - - - -Classroomndash When you are late to classhellip you run through

the hallsndash When you are earlyhellip you strut down the halls

Speed

Speed = ∆ Distance

∆ Time

Various speeds

bull These are all different numbers that have the same valueshellip they have different units of measure

bull Note Always pay close attention to units of measure your units should always agree with whats asked for in a question

To be measured

Miles per hour

Mile per second

Feet per second

Turtle 025 000006 03

Rifle bullet 2045 057 3000

Columbia shuttle

12000 33 17598

Earths orbit 40000 111 58666

bull Speed = how fast something is moving

ndash on average = over time = AVERAGE SPEED

ndashat an exact moment = INSTANTANEOUS SPEED

Average speed = Total Distance traveled Time taken

to travel Distance

bull Average speed = The average overall speed on a trip

ndashExample 2 hours in the car to travel a distance of 100 miles

ndashEquation 100 miles = 50 MPH 2 hours

bull Instantaneous speed = The speed you are traveling at that exact moment

ndashExample During a 2 hour trip over 100 miles

bull stop at a red light = 0 MPH

bull speed at 75 MPH on the highway

bull slowly driving at 25 MPH past a school

Image for remembering equations for speed math problems

VelocityVelocity = Speed and direction

ndashMeasured by a speedometer and a compass

bull Velocity = ∆ Distance + direction of movement

∆ Timebull In this class we will use the terms

interchangeablyhellip and imply the directionbull However

CONSTANT SPEED ne CONSTANT VELOCITY

The car can be traveling at the same speed but has changes in direction

bull Changes in velocity can have different causes

ndash ∆ V = same speed + ∆ direction

ndash ∆ V = ∆ speed + same direction

ndash ∆ V = ∆ speed + ∆ direction

Mathematical ndash Graphic Representations of Velocity

bull If we know the average speed we can plot the time and distance along a trip

Distances Traveled (miles)

Time (hours)

Car A at

15 MPH

Car B at

30 MPH

Car C at

60 MPH

05 75 15 30

1 15 30 60

15 225 45 90

2 30 60 120

Car Speed

0

20

40

60

80

100

120

140

0 05 1 15 2 25

Time (hours)

Dis

t m

iles

Car A

Car B

Car C

bull What do you notice about the 3 lines on the Car Speed graph

ndashSteepness of line = greater the slope of the line

ndashthe greater the slope the faster the speed of the car

ndash slope = ∆ Y or rise

∆ X run

ndash If distance is placed on the y-axis and time is placed on the x-axis

Velocity = ∆ D = ∆ Y = Slope of line

∆ T ∆ X

bull So Velocity = Slope of line

Car A Slow Gradual line

Car B Medium Medium

Car C Fast Steep line

Graphing Velocity (Average Speed)

What can you tell from different graphs

bull 3 Different objects moving at 3 different speeds

T

D

bull Stopped Object Time passes but distance does not change

bull No movement T

D

bull Backward moving objecthellip

bull The distance is decreasing so there is movement towards the source

T

D

bull Circular Motion Time passes as the same distances are revisited like a race track

T

D

bull Series of motions

bull Rest-forward-rest-backward-rest

bull Note does not represent the profile of the terrain

T

D

Velocity Graphs and Profiles of Terrain

bull What do we know about movement

bull 1 ndash rest

bull 2 ndash gradual movement forward

bull 3 ndash rest

bull 4 ndash backward movement

bull 5 ndash rest

1

2

3

4

5

T

D

Velocity Graphs and Profiles of Terrain

bull 1 ndash You are halfway up a hill at rest holding a wagon

bull 2 ndash You start moving uphillbull 3 ndash You take a restbull 4 ndash The wagon handle slips

out of you hand and travels backward down the hill

bull 5 ndash The wagon stops moving at the bottom of the hill

1

2

3

4

5

T

D

bull What could be a possible explanation pulling a wagon uphill

Dimensional Analysis ndash Unit Analysis

In your head you can probably converthellip

hellip inches to feet

sure 12 in = 1 ft

hellip inches to yards

okay 3 ft in 1 yd = 36 in

hellip inches to miles

um probably not

bull FAQ When I convert from inches to yards or yards to inches when do I multiply and when do I divide

bull The easiest way to approach these unit conversions is by using dimensional analysis

There are 4 rules1 If you use only one unit to start put it over a

12 Determine the conversion factors (Ex 12

inches = 1 ft) and put into a fraction3 Properly place the conversion factors in an

equation4 Check cancellations of units so that you are

left with the unit you were looking for on the top of a division bar The units that are canceled should be on opposite sides of the division bar

Example 1 How many feet in 13 in 1 112 or 1083 ftStep 1hellip starting with 13 sohellip 13 inches

1

Step 2hellip conversion factors 1 foot or 12 inches 12 inches 1 foot

Step 3hellip place factors 13 inches x 1 foot 1 12 inches

Step 4hellip check cancellations 13 inches x 1 foot 1 12

inches

13 inches = 1083 ft

Example 2 Convert 13 inches into yards

Step 1hellip starting with 13 sohellip 13 in

1

Step 2hellip conversion factors 1 ft 1 yd

12 in 3 ft

Step 3hellip place factors 13 in x 1 ft x 1 yd =

1 12 in 3 ft

Step 4hellip check cancellations 13 in x 1 ft x 1 yd

1 12 in 3 ft

13 in = 036 yd

Example 3 Convert 2 years into seconds

2 yrs x 365 days x 24 h x 60 min x 60 sec

1 1 yr 1 day 1 h 1 min

2 yrs = 63072000 sec

Example 4 Convert 4 decades into minutes

4 dec x 10 yrs x 365 days x 24 h x 60 min

1 1 dec 1 yr 1 day 1 h

4 decades = 21024000 m

Example 5 I am 5rsquo 3rdquo or (5 x 12) + 3 = 63 inches tall How many cm tall am I

63 in x 256 cm =

1 1 in

63 in = 1601 cm

Dimensional Analysis Worksheet

1 In New Jersey students in public schools go to school for 4 years How many minutes are students enrolled in high school

4 years x 365 days x 24 h x 60 min

1 1 yr 1 day 1 h

4 yrs = 2102400 min

2 Alaynarsquos dog is 3 ft tall What is the dogrsquos height in mm

3 ft x 12 in x 254 cm x 10 mm

1 1 ft 1 in 1 cm

3 ft = 9144 mm

3 Brian and Jesse were on a bus trip going 50 MPH For some extra fun they decided to convert the busrsquos speed into kmh What should their answer be

50 miles x 161 km 1 hr 1 mile

50 MPH = 805 kmh

4 Driving home from practice Alexrsquos mother was driving at a speed of 30 ms What was their speed in kmh

30 m x 1 km x 60 s x 60 min 1 s 1000 m 1 min 1 h

30 ms = 108 kmh

5 Saskia was riding her bike down the road at a speed of 5 kmh What was her speed in ms

5 km x 1000 m x 1 hr x 1 min 1 h 1 km 60 min 60 s

5 kmh = 139 ms

Class experiment

1 Determine how tall you are in inches

2 Using the conversion factor 1 mile = 161 km determine how tall you are in cm

3 Check your answer with a meter stick

AccelerationWhen you accelerate what are you doing

Speeding uphellip accelerating

When you slow down what are you doing

Decelerating

In physics we use the same term ldquoaccelerationrdquo for both speeding up and slowing down We distinguish between the two by assigning positive or negative values

+ acceleration as in speeding up positive

- acceleration as in slowing down negative

Acceleration = the change in velocity over time

- measured in ms or ms2

s

Acceleration = ∆ Velocity

∆ Time

Acceleration = ∆ Distance + Direction

∆ Time

∆ Time

Given an object moving in a circle

- ∆ velocity due to a ∆ direction

- if ∆ velocity the ∆ acceleration as well

- circular motion = ∆ D = ∆ V = ∆ A

Graphing Acceleration

A = ∆ V and slope = ∆ Y

∆ T ∆ X

Acceleration = ∆ V = ∆ Y = Slope of line

∆ T ∆ X

So Acceleration = Slope of line

Steep slope = fast movement

Gradual slope = slow movement

Acceleration Deceleration

V

T

V

T

Steepness of the line indicates the degree of acceleration

V

T

V

T

Comparing Velocity and Acceleration

Velocity = ∆ Distance Acceleration = ∆ Velocity

∆ Time ∆ Time

D

T

These two lines indicate the exact same thing the same rate of acceleration

bull Acceleration = + slope

bull Deceleration = - slope

T

V

+ slope

- slope

When object is a rest Velocity is zero

If ∆ Distance = 0 then ∆ Velocityhellip so Acceleration = 0

D

T

V

T

0

When acceleration equals zero

A= ∆ V no change in velocity

∆ T Time will always pass

No change in velocity

- no velocity ndash V = 0 then object is at rest

- constant velocity - ∆ V = Vfinal ndash Vinitial

Vf = 50 milesh and Vi = 50 milesh

Then ∆ V = 0

If acceleration = zero you are either stopped or on cruise control

To determine which you must find if there is a change in distance

How it all fits togetherFrom Motion Acceleration only one variable is

added at a time1 Motion = ∆ Distance2 Speed = ∆ Distance

∆ Time3 Velocity = ∆ Distance + Direction

∆ Time4 Acceleration = ∆ Distance + Direction

∆ Time∆ Time

Momentum

When an object is in motion we think velocity However we must not forget Momentum ndash which is also acting on the object

Momentum = a quantity defined as the product of an objectrsquos mass and its velocity - In a formula P = momentum- momentum moves in the same direction as the velocity

P = Mass x Velocity

- Measured in kgms

Momentum and ∆ Velocity

- large momentum difficult to change velocity

- small momentum easier to change velocity

Class Experiment Red light green light

Stationary objects have momentum of zero

Why No motion = no speed = no velocity = no momentum

Momentum is directly proportional to masshellip momentum increases as mass increases

P

Mass (kg)

Force

Force = the cause of acceleration or a change in velocity

- force is measured in units called Newtons

Net force = the combination of all the forces acting upon an object

bull The size of the arrow represents the amount of forcehellip

bull The arrows are the same so there is no movement

Friction

Friction = the force between two objects in contact that opposes the motion of either object

Pretend you are in a helicopter looking down on a ski slope in early springhellip The ice is meltinghellip Patches of dirt and gravel begin to showhellip

How much friction

Skis + snow = little frictionhellip skis move over snow

Skis + dirt = a lot of frictionhellip skis do not move over dirt

Air resistance is a type of friction

Gravity

Gravity = Force of attraction between 2 objects due to their masses

The force of gravity is different on different planets moons etc

On earth g = 98ms2

Gravity depends upon the masses as well as the distance between objects

Newtonrsquos Laws of Motion

Newtonrsquos 1st Law- the law of inertia

An object at rest remains at rest and an object in motion remains in motion unless it experiences an unbalanced force

bull Example 1 Whiplash ndash Person B is stopped at a traffic light Person A is not paying attention and rear-ends Person B

bull Result Person B moves forward suddenlyhellip Their head snaps back as it attempts to ldquoremain at restrdquo Their body attached to the seat moves forwardhellip their head snaps forward to catch up with the body resulting in whiplash

Example 2 Bus ride - The bus driver does not like children Every time they get too loud he slams on the breaks Why does he do this

Inertia = The tendency of an object to remain at rest or in motion with a constant velocity All objects have inertia because they resist changes in motion

Trivia If two people on a space ship (in space) get into a physical fight which will win

Person A Person B

Even though they are weightlesshellip there is no gravity Person A has a greater mass therefore a greater inertia

Newtonrsquos 2nd law of Motion- the law of acceleration

bull The unbalanced force acting on an object equals the objectrsquos mass times its acceleration

bull Force = Mass x Acceleration

Example pushing a cart

The greater the mass the more force needed to cause acceleration

Bumper cars

Motion

What is motion

If I threw a ball from here to there can you tell me when the ball is in motion and when it isnt

Motion = ∆ location

bull In math ∆ means change in

bull What could affect the motion of the ball

ndashHow hard I throw the ballhellip I can change the speed

bull Change in speedndash Faster means it has to go the same distance in

a shorter timendash Slower means it has to go the same distance

in a longer timebull Think about when youre running to class

Gym - - - - - - - - - - - - - - - - - - - - - -Classroomndash When you are late to classhellip you run through

the hallsndash When you are earlyhellip you strut down the halls

Speed

Speed = ∆ Distance

∆ Time

Various speeds

bull These are all different numbers that have the same valueshellip they have different units of measure

bull Note Always pay close attention to units of measure your units should always agree with whats asked for in a question

To be measured

Miles per hour

Mile per second

Feet per second

Turtle 025 000006 03

Rifle bullet 2045 057 3000

Columbia shuttle

12000 33 17598

Earths orbit 40000 111 58666

bull Speed = how fast something is moving

ndash on average = over time = AVERAGE SPEED

ndashat an exact moment = INSTANTANEOUS SPEED

Average speed = Total Distance traveled Time taken

to travel Distance

bull Average speed = The average overall speed on a trip

ndashExample 2 hours in the car to travel a distance of 100 miles

ndashEquation 100 miles = 50 MPH 2 hours

bull Instantaneous speed = The speed you are traveling at that exact moment

ndashExample During a 2 hour trip over 100 miles

bull stop at a red light = 0 MPH

bull speed at 75 MPH on the highway

bull slowly driving at 25 MPH past a school

Image for remembering equations for speed math problems

VelocityVelocity = Speed and direction

ndashMeasured by a speedometer and a compass

bull Velocity = ∆ Distance + direction of movement

∆ Timebull In this class we will use the terms

interchangeablyhellip and imply the directionbull However

CONSTANT SPEED ne CONSTANT VELOCITY

The car can be traveling at the same speed but has changes in direction

bull Changes in velocity can have different causes

ndash ∆ V = same speed + ∆ direction

ndash ∆ V = ∆ speed + same direction

ndash ∆ V = ∆ speed + ∆ direction

Mathematical ndash Graphic Representations of Velocity

bull If we know the average speed we can plot the time and distance along a trip

Distances Traveled (miles)

Time (hours)

Car A at

15 MPH

Car B at

30 MPH

Car C at

60 MPH

05 75 15 30

1 15 30 60

15 225 45 90

2 30 60 120

Car Speed

0

20

40

60

80

100

120

140

0 05 1 15 2 25

Time (hours)

Dis

t m

iles

Car A

Car B

Car C

bull What do you notice about the 3 lines on the Car Speed graph

ndashSteepness of line = greater the slope of the line

ndashthe greater the slope the faster the speed of the car

ndash slope = ∆ Y or rise

∆ X run

ndash If distance is placed on the y-axis and time is placed on the x-axis

Velocity = ∆ D = ∆ Y = Slope of line

∆ T ∆ X

bull So Velocity = Slope of line

Car A Slow Gradual line

Car B Medium Medium

Car C Fast Steep line

Graphing Velocity (Average Speed)

What can you tell from different graphs

bull 3 Different objects moving at 3 different speeds

T

D

bull Stopped Object Time passes but distance does not change

bull No movement T

D

bull Backward moving objecthellip

bull The distance is decreasing so there is movement towards the source

T

D

bull Circular Motion Time passes as the same distances are revisited like a race track

T

D

bull Series of motions

bull Rest-forward-rest-backward-rest

bull Note does not represent the profile of the terrain

T

D

Velocity Graphs and Profiles of Terrain

bull What do we know about movement

bull 1 ndash rest

bull 2 ndash gradual movement forward

bull 3 ndash rest

bull 4 ndash backward movement

bull 5 ndash rest

1

2

3

4

5

T

D

Velocity Graphs and Profiles of Terrain

bull 1 ndash You are halfway up a hill at rest holding a wagon

bull 2 ndash You start moving uphillbull 3 ndash You take a restbull 4 ndash The wagon handle slips

out of you hand and travels backward down the hill

bull 5 ndash The wagon stops moving at the bottom of the hill

1

2

3

4

5

T

D

bull What could be a possible explanation pulling a wagon uphill

Dimensional Analysis ndash Unit Analysis

In your head you can probably converthellip

hellip inches to feet

sure 12 in = 1 ft

hellip inches to yards

okay 3 ft in 1 yd = 36 in

hellip inches to miles

um probably not

bull FAQ When I convert from inches to yards or yards to inches when do I multiply and when do I divide

bull The easiest way to approach these unit conversions is by using dimensional analysis

There are 4 rules1 If you use only one unit to start put it over a

12 Determine the conversion factors (Ex 12

inches = 1 ft) and put into a fraction3 Properly place the conversion factors in an

equation4 Check cancellations of units so that you are

left with the unit you were looking for on the top of a division bar The units that are canceled should be on opposite sides of the division bar

Example 1 How many feet in 13 in 1 112 or 1083 ftStep 1hellip starting with 13 sohellip 13 inches

1

Step 2hellip conversion factors 1 foot or 12 inches 12 inches 1 foot

Step 3hellip place factors 13 inches x 1 foot 1 12 inches

Step 4hellip check cancellations 13 inches x 1 foot 1 12

inches

13 inches = 1083 ft

Example 2 Convert 13 inches into yards

Step 1hellip starting with 13 sohellip 13 in

1

Step 2hellip conversion factors 1 ft 1 yd

12 in 3 ft

Step 3hellip place factors 13 in x 1 ft x 1 yd =

1 12 in 3 ft

Step 4hellip check cancellations 13 in x 1 ft x 1 yd

1 12 in 3 ft

13 in = 036 yd

Example 3 Convert 2 years into seconds

2 yrs x 365 days x 24 h x 60 min x 60 sec

1 1 yr 1 day 1 h 1 min

2 yrs = 63072000 sec

Example 4 Convert 4 decades into minutes

4 dec x 10 yrs x 365 days x 24 h x 60 min

1 1 dec 1 yr 1 day 1 h

4 decades = 21024000 m

Example 5 I am 5rsquo 3rdquo or (5 x 12) + 3 = 63 inches tall How many cm tall am I

63 in x 256 cm =

1 1 in

63 in = 1601 cm

Dimensional Analysis Worksheet

1 In New Jersey students in public schools go to school for 4 years How many minutes are students enrolled in high school

4 years x 365 days x 24 h x 60 min

1 1 yr 1 day 1 h

4 yrs = 2102400 min

2 Alaynarsquos dog is 3 ft tall What is the dogrsquos height in mm

3 ft x 12 in x 254 cm x 10 mm

1 1 ft 1 in 1 cm

3 ft = 9144 mm

3 Brian and Jesse were on a bus trip going 50 MPH For some extra fun they decided to convert the busrsquos speed into kmh What should their answer be

50 miles x 161 km 1 hr 1 mile

50 MPH = 805 kmh

4 Driving home from practice Alexrsquos mother was driving at a speed of 30 ms What was their speed in kmh

30 m x 1 km x 60 s x 60 min 1 s 1000 m 1 min 1 h

30 ms = 108 kmh

5 Saskia was riding her bike down the road at a speed of 5 kmh What was her speed in ms

5 km x 1000 m x 1 hr x 1 min 1 h 1 km 60 min 60 s

5 kmh = 139 ms

Class experiment

1 Determine how tall you are in inches

2 Using the conversion factor 1 mile = 161 km determine how tall you are in cm

3 Check your answer with a meter stick

AccelerationWhen you accelerate what are you doing

Speeding uphellip accelerating

When you slow down what are you doing

Decelerating

In physics we use the same term ldquoaccelerationrdquo for both speeding up and slowing down We distinguish between the two by assigning positive or negative values

+ acceleration as in speeding up positive

- acceleration as in slowing down negative

Acceleration = the change in velocity over time

- measured in ms or ms2

s

Acceleration = ∆ Velocity

∆ Time

Acceleration = ∆ Distance + Direction

∆ Time

∆ Time

Given an object moving in a circle

- ∆ velocity due to a ∆ direction

- if ∆ velocity the ∆ acceleration as well

- circular motion = ∆ D = ∆ V = ∆ A

Graphing Acceleration

A = ∆ V and slope = ∆ Y

∆ T ∆ X

Acceleration = ∆ V = ∆ Y = Slope of line

∆ T ∆ X

So Acceleration = Slope of line

Steep slope = fast movement

Gradual slope = slow movement

Acceleration Deceleration

V

T

V

T

Steepness of the line indicates the degree of acceleration

V

T

V

T

Comparing Velocity and Acceleration

Velocity = ∆ Distance Acceleration = ∆ Velocity

∆ Time ∆ Time

D

T

These two lines indicate the exact same thing the same rate of acceleration

bull Acceleration = + slope

bull Deceleration = - slope

T

V

+ slope

- slope

When object is a rest Velocity is zero

If ∆ Distance = 0 then ∆ Velocityhellip so Acceleration = 0

D

T

V

T

0

When acceleration equals zero

A= ∆ V no change in velocity

∆ T Time will always pass

No change in velocity

- no velocity ndash V = 0 then object is at rest

- constant velocity - ∆ V = Vfinal ndash Vinitial

Vf = 50 milesh and Vi = 50 milesh

Then ∆ V = 0

If acceleration = zero you are either stopped or on cruise control

To determine which you must find if there is a change in distance

How it all fits togetherFrom Motion Acceleration only one variable is

added at a time1 Motion = ∆ Distance2 Speed = ∆ Distance

∆ Time3 Velocity = ∆ Distance + Direction

∆ Time4 Acceleration = ∆ Distance + Direction

∆ Time∆ Time

Momentum

When an object is in motion we think velocity However we must not forget Momentum ndash which is also acting on the object

Momentum = a quantity defined as the product of an objectrsquos mass and its velocity - In a formula P = momentum- momentum moves in the same direction as the velocity

P = Mass x Velocity

- Measured in kgms

Momentum and ∆ Velocity

- large momentum difficult to change velocity

- small momentum easier to change velocity

Class Experiment Red light green light

Stationary objects have momentum of zero

Why No motion = no speed = no velocity = no momentum

Momentum is directly proportional to masshellip momentum increases as mass increases

P

Mass (kg)

Force

Force = the cause of acceleration or a change in velocity

- force is measured in units called Newtons

Net force = the combination of all the forces acting upon an object

bull The size of the arrow represents the amount of forcehellip

bull The arrows are the same so there is no movement

Friction

Friction = the force between two objects in contact that opposes the motion of either object

Pretend you are in a helicopter looking down on a ski slope in early springhellip The ice is meltinghellip Patches of dirt and gravel begin to showhellip

How much friction

Skis + snow = little frictionhellip skis move over snow

Skis + dirt = a lot of frictionhellip skis do not move over dirt

Air resistance is a type of friction

Gravity

Gravity = Force of attraction between 2 objects due to their masses

The force of gravity is different on different planets moons etc

On earth g = 98ms2

Gravity depends upon the masses as well as the distance between objects

Newtonrsquos Laws of Motion

Newtonrsquos 1st Law- the law of inertia

An object at rest remains at rest and an object in motion remains in motion unless it experiences an unbalanced force

bull Example 1 Whiplash ndash Person B is stopped at a traffic light Person A is not paying attention and rear-ends Person B

bull Result Person B moves forward suddenlyhellip Their head snaps back as it attempts to ldquoremain at restrdquo Their body attached to the seat moves forwardhellip their head snaps forward to catch up with the body resulting in whiplash

Example 2 Bus ride - The bus driver does not like children Every time they get too loud he slams on the breaks Why does he do this

Inertia = The tendency of an object to remain at rest or in motion with a constant velocity All objects have inertia because they resist changes in motion

Trivia If two people on a space ship (in space) get into a physical fight which will win

Person A Person B

Even though they are weightlesshellip there is no gravity Person A has a greater mass therefore a greater inertia

Newtonrsquos 2nd law of Motion- the law of acceleration

bull The unbalanced force acting on an object equals the objectrsquos mass times its acceleration

bull Force = Mass x Acceleration

Example pushing a cart

The greater the mass the more force needed to cause acceleration

Bumper cars

Motion = ∆ location

bull In math ∆ means change in

bull What could affect the motion of the ball

ndashHow hard I throw the ballhellip I can change the speed

bull Change in speedndash Faster means it has to go the same distance in

a shorter timendash Slower means it has to go the same distance

in a longer timebull Think about when youre running to class

Gym - - - - - - - - - - - - - - - - - - - - - -Classroomndash When you are late to classhellip you run through

the hallsndash When you are earlyhellip you strut down the halls

Speed

Speed = ∆ Distance

∆ Time

Various speeds

bull These are all different numbers that have the same valueshellip they have different units of measure

bull Note Always pay close attention to units of measure your units should always agree with whats asked for in a question

To be measured

Miles per hour

Mile per second

Feet per second

Turtle 025 000006 03

Rifle bullet 2045 057 3000

Columbia shuttle

12000 33 17598

Earths orbit 40000 111 58666

bull Speed = how fast something is moving

ndash on average = over time = AVERAGE SPEED

ndashat an exact moment = INSTANTANEOUS SPEED

Average speed = Total Distance traveled Time taken

to travel Distance

bull Average speed = The average overall speed on a trip

ndashExample 2 hours in the car to travel a distance of 100 miles

ndashEquation 100 miles = 50 MPH 2 hours

bull Instantaneous speed = The speed you are traveling at that exact moment

ndashExample During a 2 hour trip over 100 miles

bull stop at a red light = 0 MPH

bull speed at 75 MPH on the highway

bull slowly driving at 25 MPH past a school

Image for remembering equations for speed math problems

VelocityVelocity = Speed and direction

ndashMeasured by a speedometer and a compass

bull Velocity = ∆ Distance + direction of movement

∆ Timebull In this class we will use the terms

interchangeablyhellip and imply the directionbull However

CONSTANT SPEED ne CONSTANT VELOCITY

The car can be traveling at the same speed but has changes in direction

bull Changes in velocity can have different causes

ndash ∆ V = same speed + ∆ direction

ndash ∆ V = ∆ speed + same direction

ndash ∆ V = ∆ speed + ∆ direction

Mathematical ndash Graphic Representations of Velocity

bull If we know the average speed we can plot the time and distance along a trip

Distances Traveled (miles)

Time (hours)

Car A at

15 MPH

Car B at

30 MPH

Car C at

60 MPH

05 75 15 30

1 15 30 60

15 225 45 90

2 30 60 120

Car Speed

0

20

40

60

80

100

120

140

0 05 1 15 2 25

Time (hours)

Dis

t m

iles

Car A

Car B

Car C

bull What do you notice about the 3 lines on the Car Speed graph

ndashSteepness of line = greater the slope of the line

ndashthe greater the slope the faster the speed of the car

ndash slope = ∆ Y or rise

∆ X run

ndash If distance is placed on the y-axis and time is placed on the x-axis

Velocity = ∆ D = ∆ Y = Slope of line

∆ T ∆ X

bull So Velocity = Slope of line

Car A Slow Gradual line

Car B Medium Medium

Car C Fast Steep line

Graphing Velocity (Average Speed)

What can you tell from different graphs

bull 3 Different objects moving at 3 different speeds

T

D

bull Stopped Object Time passes but distance does not change

bull No movement T

D

bull Backward moving objecthellip

bull The distance is decreasing so there is movement towards the source

T

D

bull Circular Motion Time passes as the same distances are revisited like a race track

T

D

bull Series of motions

bull Rest-forward-rest-backward-rest

bull Note does not represent the profile of the terrain

T

D

Velocity Graphs and Profiles of Terrain

bull What do we know about movement

bull 1 ndash rest

bull 2 ndash gradual movement forward

bull 3 ndash rest

bull 4 ndash backward movement

bull 5 ndash rest

1

2

3

4

5

T

D

Velocity Graphs and Profiles of Terrain

bull 1 ndash You are halfway up a hill at rest holding a wagon

bull 2 ndash You start moving uphillbull 3 ndash You take a restbull 4 ndash The wagon handle slips

out of you hand and travels backward down the hill

bull 5 ndash The wagon stops moving at the bottom of the hill

1

2

3

4

5

T

D

bull What could be a possible explanation pulling a wagon uphill

Dimensional Analysis ndash Unit Analysis

In your head you can probably converthellip

hellip inches to feet

sure 12 in = 1 ft

hellip inches to yards

okay 3 ft in 1 yd = 36 in

hellip inches to miles

um probably not

bull FAQ When I convert from inches to yards or yards to inches when do I multiply and when do I divide

bull The easiest way to approach these unit conversions is by using dimensional analysis

There are 4 rules1 If you use only one unit to start put it over a

12 Determine the conversion factors (Ex 12

inches = 1 ft) and put into a fraction3 Properly place the conversion factors in an

equation4 Check cancellations of units so that you are

left with the unit you were looking for on the top of a division bar The units that are canceled should be on opposite sides of the division bar

Example 1 How many feet in 13 in 1 112 or 1083 ftStep 1hellip starting with 13 sohellip 13 inches

1

Step 2hellip conversion factors 1 foot or 12 inches 12 inches 1 foot

Step 3hellip place factors 13 inches x 1 foot 1 12 inches

Step 4hellip check cancellations 13 inches x 1 foot 1 12

inches

13 inches = 1083 ft

Example 2 Convert 13 inches into yards

Step 1hellip starting with 13 sohellip 13 in

1

Step 2hellip conversion factors 1 ft 1 yd

12 in 3 ft

Step 3hellip place factors 13 in x 1 ft x 1 yd =

1 12 in 3 ft

Step 4hellip check cancellations 13 in x 1 ft x 1 yd

1 12 in 3 ft

13 in = 036 yd

Example 3 Convert 2 years into seconds

2 yrs x 365 days x 24 h x 60 min x 60 sec

1 1 yr 1 day 1 h 1 min

2 yrs = 63072000 sec

Example 4 Convert 4 decades into minutes

4 dec x 10 yrs x 365 days x 24 h x 60 min

1 1 dec 1 yr 1 day 1 h

4 decades = 21024000 m

Example 5 I am 5rsquo 3rdquo or (5 x 12) + 3 = 63 inches tall How many cm tall am I

63 in x 256 cm =

1 1 in

63 in = 1601 cm

Dimensional Analysis Worksheet

1 In New Jersey students in public schools go to school for 4 years How many minutes are students enrolled in high school

4 years x 365 days x 24 h x 60 min

1 1 yr 1 day 1 h

4 yrs = 2102400 min

2 Alaynarsquos dog is 3 ft tall What is the dogrsquos height in mm

3 ft x 12 in x 254 cm x 10 mm

1 1 ft 1 in 1 cm

3 ft = 9144 mm

3 Brian and Jesse were on a bus trip going 50 MPH For some extra fun they decided to convert the busrsquos speed into kmh What should their answer be

50 miles x 161 km 1 hr 1 mile

50 MPH = 805 kmh

4 Driving home from practice Alexrsquos mother was driving at a speed of 30 ms What was their speed in kmh

30 m x 1 km x 60 s x 60 min 1 s 1000 m 1 min 1 h

30 ms = 108 kmh

5 Saskia was riding her bike down the road at a speed of 5 kmh What was her speed in ms

5 km x 1000 m x 1 hr x 1 min 1 h 1 km 60 min 60 s

5 kmh = 139 ms

Class experiment

1 Determine how tall you are in inches

2 Using the conversion factor 1 mile = 161 km determine how tall you are in cm

3 Check your answer with a meter stick

AccelerationWhen you accelerate what are you doing

Speeding uphellip accelerating

When you slow down what are you doing

Decelerating

In physics we use the same term ldquoaccelerationrdquo for both speeding up and slowing down We distinguish between the two by assigning positive or negative values

+ acceleration as in speeding up positive

- acceleration as in slowing down negative

Acceleration = the change in velocity over time

- measured in ms or ms2

s

Acceleration = ∆ Velocity

∆ Time

Acceleration = ∆ Distance + Direction

∆ Time

∆ Time

Given an object moving in a circle

- ∆ velocity due to a ∆ direction

- if ∆ velocity the ∆ acceleration as well

- circular motion = ∆ D = ∆ V = ∆ A

Graphing Acceleration

A = ∆ V and slope = ∆ Y

∆ T ∆ X

Acceleration = ∆ V = ∆ Y = Slope of line

∆ T ∆ X

So Acceleration = Slope of line

Steep slope = fast movement

Gradual slope = slow movement

Acceleration Deceleration

V

T

V

T

Steepness of the line indicates the degree of acceleration

V

T

V

T

Comparing Velocity and Acceleration

Velocity = ∆ Distance Acceleration = ∆ Velocity

∆ Time ∆ Time

D

T

These two lines indicate the exact same thing the same rate of acceleration

bull Acceleration = + slope

bull Deceleration = - slope

T

V

+ slope

- slope

When object is a rest Velocity is zero

If ∆ Distance = 0 then ∆ Velocityhellip so Acceleration = 0

D

T

V

T

0

When acceleration equals zero

A= ∆ V no change in velocity

∆ T Time will always pass

No change in velocity

- no velocity ndash V = 0 then object is at rest

- constant velocity - ∆ V = Vfinal ndash Vinitial

Vf = 50 milesh and Vi = 50 milesh

Then ∆ V = 0

If acceleration = zero you are either stopped or on cruise control

To determine which you must find if there is a change in distance

How it all fits togetherFrom Motion Acceleration only one variable is

added at a time1 Motion = ∆ Distance2 Speed = ∆ Distance

∆ Time3 Velocity = ∆ Distance + Direction

∆ Time4 Acceleration = ∆ Distance + Direction

∆ Time∆ Time

Momentum

When an object is in motion we think velocity However we must not forget Momentum ndash which is also acting on the object

Momentum = a quantity defined as the product of an objectrsquos mass and its velocity - In a formula P = momentum- momentum moves in the same direction as the velocity

P = Mass x Velocity

- Measured in kgms

Momentum and ∆ Velocity

- large momentum difficult to change velocity

- small momentum easier to change velocity

Class Experiment Red light green light

Stationary objects have momentum of zero

Why No motion = no speed = no velocity = no momentum

Momentum is directly proportional to masshellip momentum increases as mass increases

P

Mass (kg)

Force

Force = the cause of acceleration or a change in velocity

- force is measured in units called Newtons

Net force = the combination of all the forces acting upon an object

bull The size of the arrow represents the amount of forcehellip

bull The arrows are the same so there is no movement

Friction

Friction = the force between two objects in contact that opposes the motion of either object

Pretend you are in a helicopter looking down on a ski slope in early springhellip The ice is meltinghellip Patches of dirt and gravel begin to showhellip

How much friction

Skis + snow = little frictionhellip skis move over snow

Skis + dirt = a lot of frictionhellip skis do not move over dirt

Air resistance is a type of friction

Gravity

Gravity = Force of attraction between 2 objects due to their masses

The force of gravity is different on different planets moons etc

On earth g = 98ms2

Gravity depends upon the masses as well as the distance between objects

Newtonrsquos Laws of Motion

Newtonrsquos 1st Law- the law of inertia

An object at rest remains at rest and an object in motion remains in motion unless it experiences an unbalanced force

bull Example 1 Whiplash ndash Person B is stopped at a traffic light Person A is not paying attention and rear-ends Person B

bull Result Person B moves forward suddenlyhellip Their head snaps back as it attempts to ldquoremain at restrdquo Their body attached to the seat moves forwardhellip their head snaps forward to catch up with the body resulting in whiplash

Example 2 Bus ride - The bus driver does not like children Every time they get too loud he slams on the breaks Why does he do this

Inertia = The tendency of an object to remain at rest or in motion with a constant velocity All objects have inertia because they resist changes in motion

Trivia If two people on a space ship (in space) get into a physical fight which will win

Person A Person B

Even though they are weightlesshellip there is no gravity Person A has a greater mass therefore a greater inertia

Newtonrsquos 2nd law of Motion- the law of acceleration

bull The unbalanced force acting on an object equals the objectrsquos mass times its acceleration

bull Force = Mass x Acceleration

Example pushing a cart

The greater the mass the more force needed to cause acceleration

Bumper cars

bull Change in speedndash Faster means it has to go the same distance in

a shorter timendash Slower means it has to go the same distance

in a longer timebull Think about when youre running to class

Gym - - - - - - - - - - - - - - - - - - - - - -Classroomndash When you are late to classhellip you run through

the hallsndash When you are earlyhellip you strut down the halls

Speed

Speed = ∆ Distance

∆ Time

Various speeds

bull These are all different numbers that have the same valueshellip they have different units of measure

bull Note Always pay close attention to units of measure your units should always agree with whats asked for in a question

To be measured

Miles per hour

Mile per second

Feet per second

Turtle 025 000006 03

Rifle bullet 2045 057 3000

Columbia shuttle

12000 33 17598

Earths orbit 40000 111 58666

bull Speed = how fast something is moving

ndash on average = over time = AVERAGE SPEED

ndashat an exact moment = INSTANTANEOUS SPEED

Average speed = Total Distance traveled Time taken

to travel Distance

bull Average speed = The average overall speed on a trip

ndashExample 2 hours in the car to travel a distance of 100 miles

ndashEquation 100 miles = 50 MPH 2 hours

bull Instantaneous speed = The speed you are traveling at that exact moment

ndashExample During a 2 hour trip over 100 miles

bull stop at a red light = 0 MPH

bull speed at 75 MPH on the highway

bull slowly driving at 25 MPH past a school

Image for remembering equations for speed math problems

VelocityVelocity = Speed and direction

ndashMeasured by a speedometer and a compass

bull Velocity = ∆ Distance + direction of movement

∆ Timebull In this class we will use the terms

interchangeablyhellip and imply the directionbull However

CONSTANT SPEED ne CONSTANT VELOCITY

The car can be traveling at the same speed but has changes in direction

bull Changes in velocity can have different causes

ndash ∆ V = same speed + ∆ direction

ndash ∆ V = ∆ speed + same direction

ndash ∆ V = ∆ speed + ∆ direction

Mathematical ndash Graphic Representations of Velocity

bull If we know the average speed we can plot the time and distance along a trip

Distances Traveled (miles)

Time (hours)

Car A at

15 MPH

Car B at

30 MPH

Car C at

60 MPH

05 75 15 30

1 15 30 60

15 225 45 90

2 30 60 120

Car Speed

0

20

40

60

80

100

120

140

0 05 1 15 2 25

Time (hours)

Dis

t m

iles

Car A

Car B

Car C

bull What do you notice about the 3 lines on the Car Speed graph

ndashSteepness of line = greater the slope of the line

ndashthe greater the slope the faster the speed of the car

ndash slope = ∆ Y or rise

∆ X run

ndash If distance is placed on the y-axis and time is placed on the x-axis

Velocity = ∆ D = ∆ Y = Slope of line

∆ T ∆ X

bull So Velocity = Slope of line

Car A Slow Gradual line

Car B Medium Medium

Car C Fast Steep line

Graphing Velocity (Average Speed)

What can you tell from different graphs

bull 3 Different objects moving at 3 different speeds

T

D

bull Stopped Object Time passes but distance does not change

bull No movement T

D

bull Backward moving objecthellip

bull The distance is decreasing so there is movement towards the source

T

D

bull Circular Motion Time passes as the same distances are revisited like a race track

T

D

bull Series of motions

bull Rest-forward-rest-backward-rest

bull Note does not represent the profile of the terrain

T

D

Velocity Graphs and Profiles of Terrain

bull What do we know about movement

bull 1 ndash rest

bull 2 ndash gradual movement forward

bull 3 ndash rest

bull 4 ndash backward movement

bull 5 ndash rest

1

2

3

4

5

T

D

Velocity Graphs and Profiles of Terrain

bull 1 ndash You are halfway up a hill at rest holding a wagon

bull 2 ndash You start moving uphillbull 3 ndash You take a restbull 4 ndash The wagon handle slips

out of you hand and travels backward down the hill

bull 5 ndash The wagon stops moving at the bottom of the hill

1

2

3

4

5

T

D

bull What could be a possible explanation pulling a wagon uphill

Dimensional Analysis ndash Unit Analysis

In your head you can probably converthellip

hellip inches to feet

sure 12 in = 1 ft

hellip inches to yards

okay 3 ft in 1 yd = 36 in

hellip inches to miles

um probably not

bull FAQ When I convert from inches to yards or yards to inches when do I multiply and when do I divide

bull The easiest way to approach these unit conversions is by using dimensional analysis

There are 4 rules1 If you use only one unit to start put it over a

12 Determine the conversion factors (Ex 12

inches = 1 ft) and put into a fraction3 Properly place the conversion factors in an

equation4 Check cancellations of units so that you are

left with the unit you were looking for on the top of a division bar The units that are canceled should be on opposite sides of the division bar

Example 1 How many feet in 13 in 1 112 or 1083 ftStep 1hellip starting with 13 sohellip 13 inches

1

Step 2hellip conversion factors 1 foot or 12 inches 12 inches 1 foot

Step 3hellip place factors 13 inches x 1 foot 1 12 inches

Step 4hellip check cancellations 13 inches x 1 foot 1 12

inches

13 inches = 1083 ft

Example 2 Convert 13 inches into yards

Step 1hellip starting with 13 sohellip 13 in

1

Step 2hellip conversion factors 1 ft 1 yd

12 in 3 ft

Step 3hellip place factors 13 in x 1 ft x 1 yd =

1 12 in 3 ft

Step 4hellip check cancellations 13 in x 1 ft x 1 yd

1 12 in 3 ft

13 in = 036 yd

Example 3 Convert 2 years into seconds

2 yrs x 365 days x 24 h x 60 min x 60 sec

1 1 yr 1 day 1 h 1 min

2 yrs = 63072000 sec

Example 4 Convert 4 decades into minutes

4 dec x 10 yrs x 365 days x 24 h x 60 min

1 1 dec 1 yr 1 day 1 h

4 decades = 21024000 m

Example 5 I am 5rsquo 3rdquo or (5 x 12) + 3 = 63 inches tall How many cm tall am I

63 in x 256 cm =

1 1 in

63 in = 1601 cm

Dimensional Analysis Worksheet

1 In New Jersey students in public schools go to school for 4 years How many minutes are students enrolled in high school

4 years x 365 days x 24 h x 60 min

1 1 yr 1 day 1 h

4 yrs = 2102400 min

2 Alaynarsquos dog is 3 ft tall What is the dogrsquos height in mm

3 ft x 12 in x 254 cm x 10 mm

1 1 ft 1 in 1 cm

3 ft = 9144 mm

3 Brian and Jesse were on a bus trip going 50 MPH For some extra fun they decided to convert the busrsquos speed into kmh What should their answer be

50 miles x 161 km 1 hr 1 mile

50 MPH = 805 kmh

4 Driving home from practice Alexrsquos mother was driving at a speed of 30 ms What was their speed in kmh

30 m x 1 km x 60 s x 60 min 1 s 1000 m 1 min 1 h

30 ms = 108 kmh

5 Saskia was riding her bike down the road at a speed of 5 kmh What was her speed in ms

5 km x 1000 m x 1 hr x 1 min 1 h 1 km 60 min 60 s

5 kmh = 139 ms

Class experiment

1 Determine how tall you are in inches

2 Using the conversion factor 1 mile = 161 km determine how tall you are in cm

3 Check your answer with a meter stick

AccelerationWhen you accelerate what are you doing

Speeding uphellip accelerating

When you slow down what are you doing

Decelerating

In physics we use the same term ldquoaccelerationrdquo for both speeding up and slowing down We distinguish between the two by assigning positive or negative values

+ acceleration as in speeding up positive

- acceleration as in slowing down negative

Acceleration = the change in velocity over time

- measured in ms or ms2

s

Acceleration = ∆ Velocity

∆ Time

Acceleration = ∆ Distance + Direction

∆ Time

∆ Time

Given an object moving in a circle

- ∆ velocity due to a ∆ direction

- if ∆ velocity the ∆ acceleration as well

- circular motion = ∆ D = ∆ V = ∆ A

Graphing Acceleration

A = ∆ V and slope = ∆ Y

∆ T ∆ X

Acceleration = ∆ V = ∆ Y = Slope of line

∆ T ∆ X

So Acceleration = Slope of line

Steep slope = fast movement

Gradual slope = slow movement

Acceleration Deceleration

V

T

V

T

Steepness of the line indicates the degree of acceleration

V

T

V

T

Comparing Velocity and Acceleration

Velocity = ∆ Distance Acceleration = ∆ Velocity

∆ Time ∆ Time

D

T

These two lines indicate the exact same thing the same rate of acceleration

bull Acceleration = + slope

bull Deceleration = - slope

T

V

+ slope

- slope

When object is a rest Velocity is zero

If ∆ Distance = 0 then ∆ Velocityhellip so Acceleration = 0

D

T

V

T

0

When acceleration equals zero

A= ∆ V no change in velocity

∆ T Time will always pass

No change in velocity

- no velocity ndash V = 0 then object is at rest

- constant velocity - ∆ V = Vfinal ndash Vinitial

Vf = 50 milesh and Vi = 50 milesh

Then ∆ V = 0

If acceleration = zero you are either stopped or on cruise control

To determine which you must find if there is a change in distance

How it all fits togetherFrom Motion Acceleration only one variable is

added at a time1 Motion = ∆ Distance2 Speed = ∆ Distance

∆ Time3 Velocity = ∆ Distance + Direction

∆ Time4 Acceleration = ∆ Distance + Direction

∆ Time∆ Time

Momentum

When an object is in motion we think velocity However we must not forget Momentum ndash which is also acting on the object

Momentum = a quantity defined as the product of an objectrsquos mass and its velocity - In a formula P = momentum- momentum moves in the same direction as the velocity

P = Mass x Velocity

- Measured in kgms

Momentum and ∆ Velocity

- large momentum difficult to change velocity

- small momentum easier to change velocity

Class Experiment Red light green light

Stationary objects have momentum of zero

Why No motion = no speed = no velocity = no momentum

Momentum is directly proportional to masshellip momentum increases as mass increases

P

Mass (kg)

Force

Force = the cause of acceleration or a change in velocity

- force is measured in units called Newtons

Net force = the combination of all the forces acting upon an object

bull The size of the arrow represents the amount of forcehellip

bull The arrows are the same so there is no movement

Friction

Friction = the force between two objects in contact that opposes the motion of either object

Pretend you are in a helicopter looking down on a ski slope in early springhellip The ice is meltinghellip Patches of dirt and gravel begin to showhellip

How much friction

Skis + snow = little frictionhellip skis move over snow

Skis + dirt = a lot of frictionhellip skis do not move over dirt

Air resistance is a type of friction

Gravity

Gravity = Force of attraction between 2 objects due to their masses

The force of gravity is different on different planets moons etc

On earth g = 98ms2

Gravity depends upon the masses as well as the distance between objects

Newtonrsquos Laws of Motion

Newtonrsquos 1st Law- the law of inertia

An object at rest remains at rest and an object in motion remains in motion unless it experiences an unbalanced force

bull Example 1 Whiplash ndash Person B is stopped at a traffic light Person A is not paying attention and rear-ends Person B

bull Result Person B moves forward suddenlyhellip Their head snaps back as it attempts to ldquoremain at restrdquo Their body attached to the seat moves forwardhellip their head snaps forward to catch up with the body resulting in whiplash

Example 2 Bus ride - The bus driver does not like children Every time they get too loud he slams on the breaks Why does he do this

Inertia = The tendency of an object to remain at rest or in motion with a constant velocity All objects have inertia because they resist changes in motion

Trivia If two people on a space ship (in space) get into a physical fight which will win

Person A Person B

Even though they are weightlesshellip there is no gravity Person A has a greater mass therefore a greater inertia

Newtonrsquos 2nd law of Motion- the law of acceleration

bull The unbalanced force acting on an object equals the objectrsquos mass times its acceleration

bull Force = Mass x Acceleration

Example pushing a cart

The greater the mass the more force needed to cause acceleration

Bumper cars

Speed

Speed = ∆ Distance

∆ Time

Various speeds

bull These are all different numbers that have the same valueshellip they have different units of measure

bull Note Always pay close attention to units of measure your units should always agree with whats asked for in a question

To be measured

Miles per hour

Mile per second

Feet per second

Turtle 025 000006 03

Rifle bullet 2045 057 3000

Columbia shuttle

12000 33 17598

Earths orbit 40000 111 58666

bull Speed = how fast something is moving

ndash on average = over time = AVERAGE SPEED

ndashat an exact moment = INSTANTANEOUS SPEED

Average speed = Total Distance traveled Time taken

to travel Distance

bull Average speed = The average overall speed on a trip

ndashExample 2 hours in the car to travel a distance of 100 miles

ndashEquation 100 miles = 50 MPH 2 hours

bull Instantaneous speed = The speed you are traveling at that exact moment

ndashExample During a 2 hour trip over 100 miles

bull stop at a red light = 0 MPH

bull speed at 75 MPH on the highway

bull slowly driving at 25 MPH past a school

Image for remembering equations for speed math problems

VelocityVelocity = Speed and direction

ndashMeasured by a speedometer and a compass

bull Velocity = ∆ Distance + direction of movement

∆ Timebull In this class we will use the terms

interchangeablyhellip and imply the directionbull However

CONSTANT SPEED ne CONSTANT VELOCITY

The car can be traveling at the same speed but has changes in direction

bull Changes in velocity can have different causes

ndash ∆ V = same speed + ∆ direction

ndash ∆ V = ∆ speed + same direction

ndash ∆ V = ∆ speed + ∆ direction

Mathematical ndash Graphic Representations of Velocity

bull If we know the average speed we can plot the time and distance along a trip

Distances Traveled (miles)

Time (hours)

Car A at

15 MPH

Car B at

30 MPH

Car C at

60 MPH

05 75 15 30

1 15 30 60

15 225 45 90

2 30 60 120

Car Speed

0

20

40

60

80

100

120

140

0 05 1 15 2 25

Time (hours)

Dis

t m

iles

Car A

Car B

Car C

bull What do you notice about the 3 lines on the Car Speed graph

ndashSteepness of line = greater the slope of the line

ndashthe greater the slope the faster the speed of the car

ndash slope = ∆ Y or rise

∆ X run

ndash If distance is placed on the y-axis and time is placed on the x-axis

Velocity = ∆ D = ∆ Y = Slope of line

∆ T ∆ X

bull So Velocity = Slope of line

Car A Slow Gradual line

Car B Medium Medium

Car C Fast Steep line

Graphing Velocity (Average Speed)

What can you tell from different graphs

bull 3 Different objects moving at 3 different speeds

T

D

bull Stopped Object Time passes but distance does not change

bull No movement T

D

bull Backward moving objecthellip

bull The distance is decreasing so there is movement towards the source

T

D

bull Circular Motion Time passes as the same distances are revisited like a race track

T

D

bull Series of motions

bull Rest-forward-rest-backward-rest

bull Note does not represent the profile of the terrain

T

D

Velocity Graphs and Profiles of Terrain

bull What do we know about movement

bull 1 ndash rest

bull 2 ndash gradual movement forward

bull 3 ndash rest

bull 4 ndash backward movement

bull 5 ndash rest

1

2

3

4

5

T

D

Velocity Graphs and Profiles of Terrain

bull 1 ndash You are halfway up a hill at rest holding a wagon

bull 2 ndash You start moving uphillbull 3 ndash You take a restbull 4 ndash The wagon handle slips

out of you hand and travels backward down the hill

bull 5 ndash The wagon stops moving at the bottom of the hill

1

2

3

4

5

T

D

bull What could be a possible explanation pulling a wagon uphill

Dimensional Analysis ndash Unit Analysis

In your head you can probably converthellip

hellip inches to feet

sure 12 in = 1 ft

hellip inches to yards

okay 3 ft in 1 yd = 36 in

hellip inches to miles

um probably not

bull FAQ When I convert from inches to yards or yards to inches when do I multiply and when do I divide

bull The easiest way to approach these unit conversions is by using dimensional analysis

There are 4 rules1 If you use only one unit to start put it over a

12 Determine the conversion factors (Ex 12

inches = 1 ft) and put into a fraction3 Properly place the conversion factors in an

equation4 Check cancellations of units so that you are

left with the unit you were looking for on the top of a division bar The units that are canceled should be on opposite sides of the division bar

Example 1 How many feet in 13 in 1 112 or 1083 ftStep 1hellip starting with 13 sohellip 13 inches

1

Step 2hellip conversion factors 1 foot or 12 inches 12 inches 1 foot

Step 3hellip place factors 13 inches x 1 foot 1 12 inches

Step 4hellip check cancellations 13 inches x 1 foot 1 12

inches

13 inches = 1083 ft

Example 2 Convert 13 inches into yards

Step 1hellip starting with 13 sohellip 13 in

1

Step 2hellip conversion factors 1 ft 1 yd

12 in 3 ft

Step 3hellip place factors 13 in x 1 ft x 1 yd =

1 12 in 3 ft

Step 4hellip check cancellations 13 in x 1 ft x 1 yd

1 12 in 3 ft

13 in = 036 yd

Example 3 Convert 2 years into seconds

2 yrs x 365 days x 24 h x 60 min x 60 sec

1 1 yr 1 day 1 h 1 min

2 yrs = 63072000 sec

Example 4 Convert 4 decades into minutes

4 dec x 10 yrs x 365 days x 24 h x 60 min

1 1 dec 1 yr 1 day 1 h

4 decades = 21024000 m

Example 5 I am 5rsquo 3rdquo or (5 x 12) + 3 = 63 inches tall How many cm tall am I

63 in x 256 cm =

1 1 in

63 in = 1601 cm

Dimensional Analysis Worksheet

1 In New Jersey students in public schools go to school for 4 years How many minutes are students enrolled in high school

4 years x 365 days x 24 h x 60 min

1 1 yr 1 day 1 h

4 yrs = 2102400 min

2 Alaynarsquos dog is 3 ft tall What is the dogrsquos height in mm

3 ft x 12 in x 254 cm x 10 mm

1 1 ft 1 in 1 cm

3 ft = 9144 mm

3 Brian and Jesse were on a bus trip going 50 MPH For some extra fun they decided to convert the busrsquos speed into kmh What should their answer be

50 miles x 161 km 1 hr 1 mile

50 MPH = 805 kmh

4 Driving home from practice Alexrsquos mother was driving at a speed of 30 ms What was their speed in kmh

30 m x 1 km x 60 s x 60 min 1 s 1000 m 1 min 1 h

30 ms = 108 kmh

5 Saskia was riding her bike down the road at a speed of 5 kmh What was her speed in ms

5 km x 1000 m x 1 hr x 1 min 1 h 1 km 60 min 60 s

5 kmh = 139 ms

Class experiment

1 Determine how tall you are in inches

2 Using the conversion factor 1 mile = 161 km determine how tall you are in cm

3 Check your answer with a meter stick

AccelerationWhen you accelerate what are you doing

Speeding uphellip accelerating

When you slow down what are you doing

Decelerating

In physics we use the same term ldquoaccelerationrdquo for both speeding up and slowing down We distinguish between the two by assigning positive or negative values

+ acceleration as in speeding up positive

- acceleration as in slowing down negative

Acceleration = the change in velocity over time

- measured in ms or ms2

s

Acceleration = ∆ Velocity

∆ Time

Acceleration = ∆ Distance + Direction

∆ Time

∆ Time

Given an object moving in a circle

- ∆ velocity due to a ∆ direction

- if ∆ velocity the ∆ acceleration as well

- circular motion = ∆ D = ∆ V = ∆ A

Graphing Acceleration

A = ∆ V and slope = ∆ Y

∆ T ∆ X

Acceleration = ∆ V = ∆ Y = Slope of line

∆ T ∆ X

So Acceleration = Slope of line

Steep slope = fast movement

Gradual slope = slow movement

Acceleration Deceleration

V

T

V

T

Steepness of the line indicates the degree of acceleration

V

T

V

T

Comparing Velocity and Acceleration

Velocity = ∆ Distance Acceleration = ∆ Velocity

∆ Time ∆ Time

D

T

These two lines indicate the exact same thing the same rate of acceleration

bull Acceleration = + slope

bull Deceleration = - slope

T

V

+ slope

- slope

When object is a rest Velocity is zero

If ∆ Distance = 0 then ∆ Velocityhellip so Acceleration = 0

D

T

V

T

0

When acceleration equals zero

A= ∆ V no change in velocity

∆ T Time will always pass

No change in velocity

- no velocity ndash V = 0 then object is at rest

- constant velocity - ∆ V = Vfinal ndash Vinitial

Vf = 50 milesh and Vi = 50 milesh

Then ∆ V = 0

If acceleration = zero you are either stopped or on cruise control

To determine which you must find if there is a change in distance

How it all fits togetherFrom Motion Acceleration only one variable is

added at a time1 Motion = ∆ Distance2 Speed = ∆ Distance

∆ Time3 Velocity = ∆ Distance + Direction

∆ Time4 Acceleration = ∆ Distance + Direction

∆ Time∆ Time

Momentum

When an object is in motion we think velocity However we must not forget Momentum ndash which is also acting on the object

Momentum = a quantity defined as the product of an objectrsquos mass and its velocity - In a formula P = momentum- momentum moves in the same direction as the velocity

P = Mass x Velocity

- Measured in kgms

Momentum and ∆ Velocity

- large momentum difficult to change velocity

- small momentum easier to change velocity

Class Experiment Red light green light

Stationary objects have momentum of zero

Why No motion = no speed = no velocity = no momentum

Momentum is directly proportional to masshellip momentum increases as mass increases

P

Mass (kg)

Force

Force = the cause of acceleration or a change in velocity

- force is measured in units called Newtons

Net force = the combination of all the forces acting upon an object

bull The size of the arrow represents the amount of forcehellip

bull The arrows are the same so there is no movement

Friction

Friction = the force between two objects in contact that opposes the motion of either object

Pretend you are in a helicopter looking down on a ski slope in early springhellip The ice is meltinghellip Patches of dirt and gravel begin to showhellip

How much friction

Skis + snow = little frictionhellip skis move over snow

Skis + dirt = a lot of frictionhellip skis do not move over dirt

Air resistance is a type of friction

Gravity

Gravity = Force of attraction between 2 objects due to their masses

The force of gravity is different on different planets moons etc

On earth g = 98ms2

Gravity depends upon the masses as well as the distance between objects

Newtonrsquos Laws of Motion

Newtonrsquos 1st Law- the law of inertia

An object at rest remains at rest and an object in motion remains in motion unless it experiences an unbalanced force

bull Example 1 Whiplash ndash Person B is stopped at a traffic light Person A is not paying attention and rear-ends Person B

bull Result Person B moves forward suddenlyhellip Their head snaps back as it attempts to ldquoremain at restrdquo Their body attached to the seat moves forwardhellip their head snaps forward to catch up with the body resulting in whiplash

Example 2 Bus ride - The bus driver does not like children Every time they get too loud he slams on the breaks Why does he do this

Inertia = The tendency of an object to remain at rest or in motion with a constant velocity All objects have inertia because they resist changes in motion

Trivia If two people on a space ship (in space) get into a physical fight which will win

Person A Person B

Even though they are weightlesshellip there is no gravity Person A has a greater mass therefore a greater inertia

Newtonrsquos 2nd law of Motion- the law of acceleration

bull The unbalanced force acting on an object equals the objectrsquos mass times its acceleration

bull Force = Mass x Acceleration

Example pushing a cart

The greater the mass the more force needed to cause acceleration

Bumper cars

Various speeds

bull These are all different numbers that have the same valueshellip they have different units of measure

bull Note Always pay close attention to units of measure your units should always agree with whats asked for in a question

To be measured

Miles per hour

Mile per second

Feet per second

Turtle 025 000006 03

Rifle bullet 2045 057 3000

Columbia shuttle

12000 33 17598

Earths orbit 40000 111 58666

bull Speed = how fast something is moving

ndash on average = over time = AVERAGE SPEED

ndashat an exact moment = INSTANTANEOUS SPEED

Average speed = Total Distance traveled Time taken

to travel Distance

bull Average speed = The average overall speed on a trip

ndashExample 2 hours in the car to travel a distance of 100 miles

ndashEquation 100 miles = 50 MPH 2 hours

bull Instantaneous speed = The speed you are traveling at that exact moment

ndashExample During a 2 hour trip over 100 miles

bull stop at a red light = 0 MPH

bull speed at 75 MPH on the highway

bull slowly driving at 25 MPH past a school

Image for remembering equations for speed math problems

VelocityVelocity = Speed and direction

ndashMeasured by a speedometer and a compass

bull Velocity = ∆ Distance + direction of movement

∆ Timebull In this class we will use the terms

interchangeablyhellip and imply the directionbull However

CONSTANT SPEED ne CONSTANT VELOCITY

The car can be traveling at the same speed but has changes in direction

bull Changes in velocity can have different causes

ndash ∆ V = same speed + ∆ direction

ndash ∆ V = ∆ speed + same direction

ndash ∆ V = ∆ speed + ∆ direction

Mathematical ndash Graphic Representations of Velocity

bull If we know the average speed we can plot the time and distance along a trip

Distances Traveled (miles)

Time (hours)

Car A at

15 MPH

Car B at

30 MPH

Car C at

60 MPH

05 75 15 30

1 15 30 60

15 225 45 90

2 30 60 120

Car Speed

0

20

40

60

80

100

120

140

0 05 1 15 2 25

Time (hours)

Dis

t m

iles

Car A

Car B

Car C

bull What do you notice about the 3 lines on the Car Speed graph

ndashSteepness of line = greater the slope of the line

ndashthe greater the slope the faster the speed of the car

ndash slope = ∆ Y or rise

∆ X run

ndash If distance is placed on the y-axis and time is placed on the x-axis

Velocity = ∆ D = ∆ Y = Slope of line

∆ T ∆ X

bull So Velocity = Slope of line

Car A Slow Gradual line

Car B Medium Medium

Car C Fast Steep line

Graphing Velocity (Average Speed)

What can you tell from different graphs

bull 3 Different objects moving at 3 different speeds

T

D

bull Stopped Object Time passes but distance does not change

bull No movement T

D

bull Backward moving objecthellip

bull The distance is decreasing so there is movement towards the source

T

D

bull Circular Motion Time passes as the same distances are revisited like a race track

T

D

bull Series of motions

bull Rest-forward-rest-backward-rest

bull Note does not represent the profile of the terrain

T

D

Velocity Graphs and Profiles of Terrain

bull What do we know about movement

bull 1 ndash rest

bull 2 ndash gradual movement forward

bull 3 ndash rest

bull 4 ndash backward movement

bull 5 ndash rest

1

2

3

4

5

T

D

Velocity Graphs and Profiles of Terrain

bull 1 ndash You are halfway up a hill at rest holding a wagon

bull 2 ndash You start moving uphillbull 3 ndash You take a restbull 4 ndash The wagon handle slips

out of you hand and travels backward down the hill

bull 5 ndash The wagon stops moving at the bottom of the hill

1

2

3

4

5

T

D

bull What could be a possible explanation pulling a wagon uphill

Dimensional Analysis ndash Unit Analysis

In your head you can probably converthellip

hellip inches to feet

sure 12 in = 1 ft

hellip inches to yards

okay 3 ft in 1 yd = 36 in

hellip inches to miles

um probably not

bull FAQ When I convert from inches to yards or yards to inches when do I multiply and when do I divide

bull The easiest way to approach these unit conversions is by using dimensional analysis

There are 4 rules1 If you use only one unit to start put it over a

12 Determine the conversion factors (Ex 12

inches = 1 ft) and put into a fraction3 Properly place the conversion factors in an

equation4 Check cancellations of units so that you are

left with the unit you were looking for on the top of a division bar The units that are canceled should be on opposite sides of the division bar

Example 1 How many feet in 13 in 1 112 or 1083 ftStep 1hellip starting with 13 sohellip 13 inches

1

Step 2hellip conversion factors 1 foot or 12 inches 12 inches 1 foot

Step 3hellip place factors 13 inches x 1 foot 1 12 inches

Step 4hellip check cancellations 13 inches x 1 foot 1 12

inches

13 inches = 1083 ft

Example 2 Convert 13 inches into yards

Step 1hellip starting with 13 sohellip 13 in

1

Step 2hellip conversion factors 1 ft 1 yd

12 in 3 ft

Step 3hellip place factors 13 in x 1 ft x 1 yd =

1 12 in 3 ft

Step 4hellip check cancellations 13 in x 1 ft x 1 yd

1 12 in 3 ft

13 in = 036 yd

Example 3 Convert 2 years into seconds

2 yrs x 365 days x 24 h x 60 min x 60 sec

1 1 yr 1 day 1 h 1 min

2 yrs = 63072000 sec

Example 4 Convert 4 decades into minutes

4 dec x 10 yrs x 365 days x 24 h x 60 min

1 1 dec 1 yr 1 day 1 h

4 decades = 21024000 m

Example 5 I am 5rsquo 3rdquo or (5 x 12) + 3 = 63 inches tall How many cm tall am I

63 in x 256 cm =

1 1 in

63 in = 1601 cm

Dimensional Analysis Worksheet

1 In New Jersey students in public schools go to school for 4 years How many minutes are students enrolled in high school

4 years x 365 days x 24 h x 60 min

1 1 yr 1 day 1 h

4 yrs = 2102400 min

2 Alaynarsquos dog is 3 ft tall What is the dogrsquos height in mm

3 ft x 12 in x 254 cm x 10 mm

1 1 ft 1 in 1 cm

3 ft = 9144 mm

3 Brian and Jesse were on a bus trip going 50 MPH For some extra fun they decided to convert the busrsquos speed into kmh What should their answer be

50 miles x 161 km 1 hr 1 mile

50 MPH = 805 kmh

4 Driving home from practice Alexrsquos mother was driving at a speed of 30 ms What was their speed in kmh

30 m x 1 km x 60 s x 60 min 1 s 1000 m 1 min 1 h

30 ms = 108 kmh

5 Saskia was riding her bike down the road at a speed of 5 kmh What was her speed in ms

5 km x 1000 m x 1 hr x 1 min 1 h 1 km 60 min 60 s

5 kmh = 139 ms

Class experiment

1 Determine how tall you are in inches

2 Using the conversion factor 1 mile = 161 km determine how tall you are in cm

3 Check your answer with a meter stick

AccelerationWhen you accelerate what are you doing

Speeding uphellip accelerating

When you slow down what are you doing

Decelerating

In physics we use the same term ldquoaccelerationrdquo for both speeding up and slowing down We distinguish between the two by assigning positive or negative values

+ acceleration as in speeding up positive

- acceleration as in slowing down negative

Acceleration = the change in velocity over time

- measured in ms or ms2

s

Acceleration = ∆ Velocity

∆ Time

Acceleration = ∆ Distance + Direction

∆ Time

∆ Time

Given an object moving in a circle

- ∆ velocity due to a ∆ direction

- if ∆ velocity the ∆ acceleration as well

- circular motion = ∆ D = ∆ V = ∆ A

Graphing Acceleration

A = ∆ V and slope = ∆ Y

∆ T ∆ X

Acceleration = ∆ V = ∆ Y = Slope of line

∆ T ∆ X

So Acceleration = Slope of line

Steep slope = fast movement

Gradual slope = slow movement

Acceleration Deceleration

V

T

V

T

Steepness of the line indicates the degree of acceleration

V

T

V

T

Comparing Velocity and Acceleration

Velocity = ∆ Distance Acceleration = ∆ Velocity

∆ Time ∆ Time

D

T

These two lines indicate the exact same thing the same rate of acceleration

bull Acceleration = + slope

bull Deceleration = - slope

T

V

+ slope

- slope

When object is a rest Velocity is zero

If ∆ Distance = 0 then ∆ Velocityhellip so Acceleration = 0

D

T

V

T

0

When acceleration equals zero

A= ∆ V no change in velocity

∆ T Time will always pass

No change in velocity

- no velocity ndash V = 0 then object is at rest

- constant velocity - ∆ V = Vfinal ndash Vinitial

Vf = 50 milesh and Vi = 50 milesh

Then ∆ V = 0

If acceleration = zero you are either stopped or on cruise control

To determine which you must find if there is a change in distance

How it all fits togetherFrom Motion Acceleration only one variable is

added at a time1 Motion = ∆ Distance2 Speed = ∆ Distance

∆ Time3 Velocity = ∆ Distance + Direction

∆ Time4 Acceleration = ∆ Distance + Direction

∆ Time∆ Time

Momentum

When an object is in motion we think velocity However we must not forget Momentum ndash which is also acting on the object

Momentum = a quantity defined as the product of an objectrsquos mass and its velocity - In a formula P = momentum- momentum moves in the same direction as the velocity

P = Mass x Velocity

- Measured in kgms

Momentum and ∆ Velocity

- large momentum difficult to change velocity

- small momentum easier to change velocity

Class Experiment Red light green light

Stationary objects have momentum of zero

Why No motion = no speed = no velocity = no momentum

Momentum is directly proportional to masshellip momentum increases as mass increases

P

Mass (kg)

Force

Force = the cause of acceleration or a change in velocity

- force is measured in units called Newtons

Net force = the combination of all the forces acting upon an object

bull The size of the arrow represents the amount of forcehellip

bull The arrows are the same so there is no movement

Friction

Friction = the force between two objects in contact that opposes the motion of either object

Pretend you are in a helicopter looking down on a ski slope in early springhellip The ice is meltinghellip Patches of dirt and gravel begin to showhellip

How much friction

Skis + snow = little frictionhellip skis move over snow

Skis + dirt = a lot of frictionhellip skis do not move over dirt

Air resistance is a type of friction

Gravity

Gravity = Force of attraction between 2 objects due to their masses

The force of gravity is different on different planets moons etc

On earth g = 98ms2

Gravity depends upon the masses as well as the distance between objects

Newtonrsquos Laws of Motion

Newtonrsquos 1st Law- the law of inertia

An object at rest remains at rest and an object in motion remains in motion unless it experiences an unbalanced force

bull Example 1 Whiplash ndash Person B is stopped at a traffic light Person A is not paying attention and rear-ends Person B

bull Result Person B moves forward suddenlyhellip Their head snaps back as it attempts to ldquoremain at restrdquo Their body attached to the seat moves forwardhellip their head snaps forward to catch up with the body resulting in whiplash

Example 2 Bus ride - The bus driver does not like children Every time they get too loud he slams on the breaks Why does he do this

Inertia = The tendency of an object to remain at rest or in motion with a constant velocity All objects have inertia because they resist changes in motion

Trivia If two people on a space ship (in space) get into a physical fight which will win

Person A Person B

Even though they are weightlesshellip there is no gravity Person A has a greater mass therefore a greater inertia

Newtonrsquos 2nd law of Motion- the law of acceleration

bull The unbalanced force acting on an object equals the objectrsquos mass times its acceleration

bull Force = Mass x Acceleration

Example pushing a cart

The greater the mass the more force needed to cause acceleration

Bumper cars

bull Speed = how fast something is moving

ndash on average = over time = AVERAGE SPEED

ndashat an exact moment = INSTANTANEOUS SPEED

Average speed = Total Distance traveled Time taken

to travel Distance

bull Average speed = The average overall speed on a trip

ndashExample 2 hours in the car to travel a distance of 100 miles

ndashEquation 100 miles = 50 MPH 2 hours

bull Instantaneous speed = The speed you are traveling at that exact moment

ndashExample During a 2 hour trip over 100 miles

bull stop at a red light = 0 MPH

bull speed at 75 MPH on the highway

bull slowly driving at 25 MPH past a school

Image for remembering equations for speed math problems

VelocityVelocity = Speed and direction

ndashMeasured by a speedometer and a compass

bull Velocity = ∆ Distance + direction of movement

∆ Timebull In this class we will use the terms

interchangeablyhellip and imply the directionbull However

CONSTANT SPEED ne CONSTANT VELOCITY

The car can be traveling at the same speed but has changes in direction

bull Changes in velocity can have different causes

ndash ∆ V = same speed + ∆ direction

ndash ∆ V = ∆ speed + same direction

ndash ∆ V = ∆ speed + ∆ direction

Mathematical ndash Graphic Representations of Velocity

bull If we know the average speed we can plot the time and distance along a trip

Distances Traveled (miles)

Time (hours)

Car A at

15 MPH

Car B at

30 MPH

Car C at

60 MPH

05 75 15 30

1 15 30 60

15 225 45 90

2 30 60 120

Car Speed

0

20

40

60

80

100

120

140

0 05 1 15 2 25

Time (hours)

Dis

t m

iles

Car A

Car B

Car C

bull What do you notice about the 3 lines on the Car Speed graph

ndashSteepness of line = greater the slope of the line

ndashthe greater the slope the faster the speed of the car

ndash slope = ∆ Y or rise

∆ X run

ndash If distance is placed on the y-axis and time is placed on the x-axis

Velocity = ∆ D = ∆ Y = Slope of line

∆ T ∆ X

bull So Velocity = Slope of line

Car A Slow Gradual line

Car B Medium Medium

Car C Fast Steep line

Graphing Velocity (Average Speed)

What can you tell from different graphs

bull 3 Different objects moving at 3 different speeds

T

D

bull Stopped Object Time passes but distance does not change

bull No movement T

D

bull Backward moving objecthellip

bull The distance is decreasing so there is movement towards the source

T

D

bull Circular Motion Time passes as the same distances are revisited like a race track

T

D

bull Series of motions

bull Rest-forward-rest-backward-rest

bull Note does not represent the profile of the terrain

T

D

Velocity Graphs and Profiles of Terrain

bull What do we know about movement

bull 1 ndash rest

bull 2 ndash gradual movement forward

bull 3 ndash rest

bull 4 ndash backward movement

bull 5 ndash rest

1

2

3

4

5

T

D

Velocity Graphs and Profiles of Terrain

bull 1 ndash You are halfway up a hill at rest holding a wagon

bull 2 ndash You start moving uphillbull 3 ndash You take a restbull 4 ndash The wagon handle slips

out of you hand and travels backward down the hill

bull 5 ndash The wagon stops moving at the bottom of the hill

1

2

3

4

5

T

D

bull What could be a possible explanation pulling a wagon uphill

Dimensional Analysis ndash Unit Analysis

In your head you can probably converthellip

hellip inches to feet

sure 12 in = 1 ft

hellip inches to yards

okay 3 ft in 1 yd = 36 in

hellip inches to miles

um probably not

bull FAQ When I convert from inches to yards or yards to inches when do I multiply and when do I divide

bull The easiest way to approach these unit conversions is by using dimensional analysis

There are 4 rules1 If you use only one unit to start put it over a

12 Determine the conversion factors (Ex 12

inches = 1 ft) and put into a fraction3 Properly place the conversion factors in an

equation4 Check cancellations of units so that you are

left with the unit you were looking for on the top of a division bar The units that are canceled should be on opposite sides of the division bar

Example 1 How many feet in 13 in 1 112 or 1083 ftStep 1hellip starting with 13 sohellip 13 inches

1

Step 2hellip conversion factors 1 foot or 12 inches 12 inches 1 foot

Step 3hellip place factors 13 inches x 1 foot 1 12 inches

Step 4hellip check cancellations 13 inches x 1 foot 1 12

inches

13 inches = 1083 ft

Example 2 Convert 13 inches into yards

Step 1hellip starting with 13 sohellip 13 in

1

Step 2hellip conversion factors 1 ft 1 yd

12 in 3 ft

Step 3hellip place factors 13 in x 1 ft x 1 yd =

1 12 in 3 ft

Step 4hellip check cancellations 13 in x 1 ft x 1 yd

1 12 in 3 ft

13 in = 036 yd

Example 3 Convert 2 years into seconds

2 yrs x 365 days x 24 h x 60 min x 60 sec

1 1 yr 1 day 1 h 1 min

2 yrs = 63072000 sec

Example 4 Convert 4 decades into minutes

4 dec x 10 yrs x 365 days x 24 h x 60 min

1 1 dec 1 yr 1 day 1 h

4 decades = 21024000 m

Example 5 I am 5rsquo 3rdquo or (5 x 12) + 3 = 63 inches tall How many cm tall am I

63 in x 256 cm =

1 1 in

63 in = 1601 cm

Dimensional Analysis Worksheet

1 In New Jersey students in public schools go to school for 4 years How many minutes are students enrolled in high school

4 years x 365 days x 24 h x 60 min

1 1 yr 1 day 1 h

4 yrs = 2102400 min

2 Alaynarsquos dog is 3 ft tall What is the dogrsquos height in mm

3 ft x 12 in x 254 cm x 10 mm

1 1 ft 1 in 1 cm

3 ft = 9144 mm

3 Brian and Jesse were on a bus trip going 50 MPH For some extra fun they decided to convert the busrsquos speed into kmh What should their answer be

50 miles x 161 km 1 hr 1 mile

50 MPH = 805 kmh

4 Driving home from practice Alexrsquos mother was driving at a speed of 30 ms What was their speed in kmh

30 m x 1 km x 60 s x 60 min 1 s 1000 m 1 min 1 h

30 ms = 108 kmh

5 Saskia was riding her bike down the road at a speed of 5 kmh What was her speed in ms

5 km x 1000 m x 1 hr x 1 min 1 h 1 km 60 min 60 s

5 kmh = 139 ms

Class experiment

1 Determine how tall you are in inches

2 Using the conversion factor 1 mile = 161 km determine how tall you are in cm

3 Check your answer with a meter stick

AccelerationWhen you accelerate what are you doing

Speeding uphellip accelerating

When you slow down what are you doing

Decelerating

In physics we use the same term ldquoaccelerationrdquo for both speeding up and slowing down We distinguish between the two by assigning positive or negative values

+ acceleration as in speeding up positive

- acceleration as in slowing down negative

Acceleration = the change in velocity over time

- measured in ms or ms2

s

Acceleration = ∆ Velocity

∆ Time

Acceleration = ∆ Distance + Direction

∆ Time

∆ Time

Given an object moving in a circle

- ∆ velocity due to a ∆ direction

- if ∆ velocity the ∆ acceleration as well

- circular motion = ∆ D = ∆ V = ∆ A

Graphing Acceleration

A = ∆ V and slope = ∆ Y

∆ T ∆ X

Acceleration = ∆ V = ∆ Y = Slope of line

∆ T ∆ X

So Acceleration = Slope of line

Steep slope = fast movement

Gradual slope = slow movement

Acceleration Deceleration

V

T

V

T

Steepness of the line indicates the degree of acceleration

V

T

V

T

Comparing Velocity and Acceleration

Velocity = ∆ Distance Acceleration = ∆ Velocity

∆ Time ∆ Time

D

T

These two lines indicate the exact same thing the same rate of acceleration

bull Acceleration = + slope

bull Deceleration = - slope

T

V

+ slope

- slope

When object is a rest Velocity is zero

If ∆ Distance = 0 then ∆ Velocityhellip so Acceleration = 0

D

T

V

T

0

When acceleration equals zero

A= ∆ V no change in velocity

∆ T Time will always pass

No change in velocity

- no velocity ndash V = 0 then object is at rest

- constant velocity - ∆ V = Vfinal ndash Vinitial

Vf = 50 milesh and Vi = 50 milesh

Then ∆ V = 0

If acceleration = zero you are either stopped or on cruise control

To determine which you must find if there is a change in distance

How it all fits togetherFrom Motion Acceleration only one variable is

added at a time1 Motion = ∆ Distance2 Speed = ∆ Distance

∆ Time3 Velocity = ∆ Distance + Direction

∆ Time4 Acceleration = ∆ Distance + Direction

∆ Time∆ Time

Momentum

When an object is in motion we think velocity However we must not forget Momentum ndash which is also acting on the object

Momentum = a quantity defined as the product of an objectrsquos mass and its velocity - In a formula P = momentum- momentum moves in the same direction as the velocity

P = Mass x Velocity

- Measured in kgms

Momentum and ∆ Velocity

- large momentum difficult to change velocity

- small momentum easier to change velocity

Class Experiment Red light green light

Stationary objects have momentum of zero

Why No motion = no speed = no velocity = no momentum

Momentum is directly proportional to masshellip momentum increases as mass increases

P

Mass (kg)

Force

Force = the cause of acceleration or a change in velocity

- force is measured in units called Newtons

Net force = the combination of all the forces acting upon an object

bull The size of the arrow represents the amount of forcehellip

bull The arrows are the same so there is no movement

Friction

Friction = the force between two objects in contact that opposes the motion of either object

Pretend you are in a helicopter looking down on a ski slope in early springhellip The ice is meltinghellip Patches of dirt and gravel begin to showhellip

How much friction

Skis + snow = little frictionhellip skis move over snow

Skis + dirt = a lot of frictionhellip skis do not move over dirt

Air resistance is a type of friction

Gravity

Gravity = Force of attraction between 2 objects due to their masses

The force of gravity is different on different planets moons etc

On earth g = 98ms2

Gravity depends upon the masses as well as the distance between objects

Newtonrsquos Laws of Motion

Newtonrsquos 1st Law- the law of inertia

An object at rest remains at rest and an object in motion remains in motion unless it experiences an unbalanced force

bull Example 1 Whiplash ndash Person B is stopped at a traffic light Person A is not paying attention and rear-ends Person B

bull Result Person B moves forward suddenlyhellip Their head snaps back as it attempts to ldquoremain at restrdquo Their body attached to the seat moves forwardhellip their head snaps forward to catch up with the body resulting in whiplash

Example 2 Bus ride - The bus driver does not like children Every time they get too loud he slams on the breaks Why does he do this

Inertia = The tendency of an object to remain at rest or in motion with a constant velocity All objects have inertia because they resist changes in motion

Trivia If two people on a space ship (in space) get into a physical fight which will win

Person A Person B

Even though they are weightlesshellip there is no gravity Person A has a greater mass therefore a greater inertia

Newtonrsquos 2nd law of Motion- the law of acceleration

bull The unbalanced force acting on an object equals the objectrsquos mass times its acceleration

bull Force = Mass x Acceleration

Example pushing a cart

The greater the mass the more force needed to cause acceleration

Bumper cars

Average speed = Total Distance traveled Time taken

to travel Distance

bull Average speed = The average overall speed on a trip

ndashExample 2 hours in the car to travel a distance of 100 miles

ndashEquation 100 miles = 50 MPH 2 hours

bull Instantaneous speed = The speed you are traveling at that exact moment

ndashExample During a 2 hour trip over 100 miles

bull stop at a red light = 0 MPH

bull speed at 75 MPH on the highway

bull slowly driving at 25 MPH past a school

Image for remembering equations for speed math problems

VelocityVelocity = Speed and direction

ndashMeasured by a speedometer and a compass

bull Velocity = ∆ Distance + direction of movement

∆ Timebull In this class we will use the terms

interchangeablyhellip and imply the directionbull However

CONSTANT SPEED ne CONSTANT VELOCITY

The car can be traveling at the same speed but has changes in direction

bull Changes in velocity can have different causes

ndash ∆ V = same speed + ∆ direction

ndash ∆ V = ∆ speed + same direction

ndash ∆ V = ∆ speed + ∆ direction

Mathematical ndash Graphic Representations of Velocity

bull If we know the average speed we can plot the time and distance along a trip

Distances Traveled (miles)

Time (hours)

Car A at

15 MPH

Car B at

30 MPH

Car C at

60 MPH

05 75 15 30

1 15 30 60

15 225 45 90

2 30 60 120

Car Speed

0

20

40

60

80

100

120

140

0 05 1 15 2 25

Time (hours)

Dis

t m

iles

Car A

Car B

Car C

bull What do you notice about the 3 lines on the Car Speed graph

ndashSteepness of line = greater the slope of the line

ndashthe greater the slope the faster the speed of the car

ndash slope = ∆ Y or rise

∆ X run

ndash If distance is placed on the y-axis and time is placed on the x-axis

Velocity = ∆ D = ∆ Y = Slope of line

∆ T ∆ X

bull So Velocity = Slope of line

Car A Slow Gradual line

Car B Medium Medium

Car C Fast Steep line

Graphing Velocity (Average Speed)

What can you tell from different graphs

bull 3 Different objects moving at 3 different speeds

T

D

bull Stopped Object Time passes but distance does not change

bull No movement T

D

bull Backward moving objecthellip

bull The distance is decreasing so there is movement towards the source

T

D

bull Circular Motion Time passes as the same distances are revisited like a race track

T

D

bull Series of motions

bull Rest-forward-rest-backward-rest

bull Note does not represent the profile of the terrain

T

D

Velocity Graphs and Profiles of Terrain

bull What do we know about movement

bull 1 ndash rest

bull 2 ndash gradual movement forward

bull 3 ndash rest

bull 4 ndash backward movement

bull 5 ndash rest

1

2

3

4

5

T

D

Velocity Graphs and Profiles of Terrain

bull 1 ndash You are halfway up a hill at rest holding a wagon

bull 2 ndash You start moving uphillbull 3 ndash You take a restbull 4 ndash The wagon handle slips

out of you hand and travels backward down the hill

bull 5 ndash The wagon stops moving at the bottom of the hill

1

2

3

4

5

T

D

bull What could be a possible explanation pulling a wagon uphill

Dimensional Analysis ndash Unit Analysis

In your head you can probably converthellip

hellip inches to feet

sure 12 in = 1 ft

hellip inches to yards

okay 3 ft in 1 yd = 36 in

hellip inches to miles

um probably not

bull FAQ When I convert from inches to yards or yards to inches when do I multiply and when do I divide

bull The easiest way to approach these unit conversions is by using dimensional analysis

There are 4 rules1 If you use only one unit to start put it over a

12 Determine the conversion factors (Ex 12

inches = 1 ft) and put into a fraction3 Properly place the conversion factors in an

equation4 Check cancellations of units so that you are

left with the unit you were looking for on the top of a division bar The units that are canceled should be on opposite sides of the division bar

Example 1 How many feet in 13 in 1 112 or 1083 ftStep 1hellip starting with 13 sohellip 13 inches

1

Step 2hellip conversion factors 1 foot or 12 inches 12 inches 1 foot

Step 3hellip place factors 13 inches x 1 foot 1 12 inches

Step 4hellip check cancellations 13 inches x 1 foot 1 12

inches

13 inches = 1083 ft

Example 2 Convert 13 inches into yards

Step 1hellip starting with 13 sohellip 13 in

1

Step 2hellip conversion factors 1 ft 1 yd

12 in 3 ft

Step 3hellip place factors 13 in x 1 ft x 1 yd =

1 12 in 3 ft

Step 4hellip check cancellations 13 in x 1 ft x 1 yd

1 12 in 3 ft

13 in = 036 yd

Example 3 Convert 2 years into seconds

2 yrs x 365 days x 24 h x 60 min x 60 sec

1 1 yr 1 day 1 h 1 min

2 yrs = 63072000 sec

Example 4 Convert 4 decades into minutes

4 dec x 10 yrs x 365 days x 24 h x 60 min

1 1 dec 1 yr 1 day 1 h

4 decades = 21024000 m

Example 5 I am 5rsquo 3rdquo or (5 x 12) + 3 = 63 inches tall How many cm tall am I

63 in x 256 cm =

1 1 in

63 in = 1601 cm

Dimensional Analysis Worksheet

1 In New Jersey students in public schools go to school for 4 years How many minutes are students enrolled in high school

4 years x 365 days x 24 h x 60 min

1 1 yr 1 day 1 h

4 yrs = 2102400 min

2 Alaynarsquos dog is 3 ft tall What is the dogrsquos height in mm

3 ft x 12 in x 254 cm x 10 mm

1 1 ft 1 in 1 cm

3 ft = 9144 mm

3 Brian and Jesse were on a bus trip going 50 MPH For some extra fun they decided to convert the busrsquos speed into kmh What should their answer be

50 miles x 161 km 1 hr 1 mile

50 MPH = 805 kmh

4 Driving home from practice Alexrsquos mother was driving at a speed of 30 ms What was their speed in kmh

30 m x 1 km x 60 s x 60 min 1 s 1000 m 1 min 1 h

30 ms = 108 kmh

5 Saskia was riding her bike down the road at a speed of 5 kmh What was her speed in ms

5 km x 1000 m x 1 hr x 1 min 1 h 1 km 60 min 60 s

5 kmh = 139 ms

Class experiment

1 Determine how tall you are in inches

2 Using the conversion factor 1 mile = 161 km determine how tall you are in cm

3 Check your answer with a meter stick

AccelerationWhen you accelerate what are you doing

Speeding uphellip accelerating

When you slow down what are you doing

Decelerating

In physics we use the same term ldquoaccelerationrdquo for both speeding up and slowing down We distinguish between the two by assigning positive or negative values

+ acceleration as in speeding up positive

- acceleration as in slowing down negative

Acceleration = the change in velocity over time

- measured in ms or ms2

s

Acceleration = ∆ Velocity

∆ Time

Acceleration = ∆ Distance + Direction

∆ Time

∆ Time

Given an object moving in a circle

- ∆ velocity due to a ∆ direction

- if ∆ velocity the ∆ acceleration as well

- circular motion = ∆ D = ∆ V = ∆ A

Graphing Acceleration

A = ∆ V and slope = ∆ Y

∆ T ∆ X

Acceleration = ∆ V = ∆ Y = Slope of line

∆ T ∆ X

So Acceleration = Slope of line

Steep slope = fast movement

Gradual slope = slow movement

Acceleration Deceleration

V

T

V

T

Steepness of the line indicates the degree of acceleration

V

T

V

T

Comparing Velocity and Acceleration

Velocity = ∆ Distance Acceleration = ∆ Velocity

∆ Time ∆ Time

D

T

These two lines indicate the exact same thing the same rate of acceleration

bull Acceleration = + slope

bull Deceleration = - slope

T

V

+ slope

- slope

When object is a rest Velocity is zero

If ∆ Distance = 0 then ∆ Velocityhellip so Acceleration = 0

D

T

V

T

0

When acceleration equals zero

A= ∆ V no change in velocity

∆ T Time will always pass

No change in velocity

- no velocity ndash V = 0 then object is at rest

- constant velocity - ∆ V = Vfinal ndash Vinitial

Vf = 50 milesh and Vi = 50 milesh

Then ∆ V = 0

If acceleration = zero you are either stopped or on cruise control

To determine which you must find if there is a change in distance

How it all fits togetherFrom Motion Acceleration only one variable is

added at a time1 Motion = ∆ Distance2 Speed = ∆ Distance

∆ Time3 Velocity = ∆ Distance + Direction

∆ Time4 Acceleration = ∆ Distance + Direction

∆ Time∆ Time

Momentum

When an object is in motion we think velocity However we must not forget Momentum ndash which is also acting on the object

Momentum = a quantity defined as the product of an objectrsquos mass and its velocity - In a formula P = momentum- momentum moves in the same direction as the velocity

P = Mass x Velocity

- Measured in kgms

Momentum and ∆ Velocity

- large momentum difficult to change velocity

- small momentum easier to change velocity

Class Experiment Red light green light

Stationary objects have momentum of zero

Why No motion = no speed = no velocity = no momentum

Momentum is directly proportional to masshellip momentum increases as mass increases

P

Mass (kg)

Force

Force = the cause of acceleration or a change in velocity

- force is measured in units called Newtons

Net force = the combination of all the forces acting upon an object

bull The size of the arrow represents the amount of forcehellip

bull The arrows are the same so there is no movement

Friction

Friction = the force between two objects in contact that opposes the motion of either object

Pretend you are in a helicopter looking down on a ski slope in early springhellip The ice is meltinghellip Patches of dirt and gravel begin to showhellip

How much friction

Skis + snow = little frictionhellip skis move over snow

Skis + dirt = a lot of frictionhellip skis do not move over dirt

Air resistance is a type of friction

Gravity

Gravity = Force of attraction between 2 objects due to their masses

The force of gravity is different on different planets moons etc

On earth g = 98ms2

Gravity depends upon the masses as well as the distance between objects

Newtonrsquos Laws of Motion

Newtonrsquos 1st Law- the law of inertia

An object at rest remains at rest and an object in motion remains in motion unless it experiences an unbalanced force

bull Example 1 Whiplash ndash Person B is stopped at a traffic light Person A is not paying attention and rear-ends Person B

bull Result Person B moves forward suddenlyhellip Their head snaps back as it attempts to ldquoremain at restrdquo Their body attached to the seat moves forwardhellip their head snaps forward to catch up with the body resulting in whiplash

Example 2 Bus ride - The bus driver does not like children Every time they get too loud he slams on the breaks Why does he do this

Inertia = The tendency of an object to remain at rest or in motion with a constant velocity All objects have inertia because they resist changes in motion

Trivia If two people on a space ship (in space) get into a physical fight which will win

Person A Person B

Even though they are weightlesshellip there is no gravity Person A has a greater mass therefore a greater inertia

Newtonrsquos 2nd law of Motion- the law of acceleration

bull The unbalanced force acting on an object equals the objectrsquos mass times its acceleration

bull Force = Mass x Acceleration

Example pushing a cart

The greater the mass the more force needed to cause acceleration

Bumper cars

bull Instantaneous speed = The speed you are traveling at that exact moment

ndashExample During a 2 hour trip over 100 miles

bull stop at a red light = 0 MPH

bull speed at 75 MPH on the highway

bull slowly driving at 25 MPH past a school

Image for remembering equations for speed math problems

VelocityVelocity = Speed and direction

ndashMeasured by a speedometer and a compass

bull Velocity = ∆ Distance + direction of movement

∆ Timebull In this class we will use the terms

interchangeablyhellip and imply the directionbull However

CONSTANT SPEED ne CONSTANT VELOCITY

The car can be traveling at the same speed but has changes in direction

bull Changes in velocity can have different causes

ndash ∆ V = same speed + ∆ direction

ndash ∆ V = ∆ speed + same direction

ndash ∆ V = ∆ speed + ∆ direction

Mathematical ndash Graphic Representations of Velocity

bull If we know the average speed we can plot the time and distance along a trip

Distances Traveled (miles)

Time (hours)

Car A at

15 MPH

Car B at

30 MPH

Car C at

60 MPH

05 75 15 30

1 15 30 60

15 225 45 90

2 30 60 120

Car Speed

0

20

40

60

80

100

120

140

0 05 1 15 2 25

Time (hours)

Dis

t m

iles

Car A

Car B

Car C

bull What do you notice about the 3 lines on the Car Speed graph

ndashSteepness of line = greater the slope of the line

ndashthe greater the slope the faster the speed of the car

ndash slope = ∆ Y or rise

∆ X run

ndash If distance is placed on the y-axis and time is placed on the x-axis

Velocity = ∆ D = ∆ Y = Slope of line

∆ T ∆ X

bull So Velocity = Slope of line

Car A Slow Gradual line

Car B Medium Medium

Car C Fast Steep line

Graphing Velocity (Average Speed)

What can you tell from different graphs

bull 3 Different objects moving at 3 different speeds

T

D

bull Stopped Object Time passes but distance does not change

bull No movement T

D

bull Backward moving objecthellip

bull The distance is decreasing so there is movement towards the source

T

D

bull Circular Motion Time passes as the same distances are revisited like a race track

T

D

bull Series of motions

bull Rest-forward-rest-backward-rest

bull Note does not represent the profile of the terrain

T

D

Velocity Graphs and Profiles of Terrain

bull What do we know about movement

bull 1 ndash rest

bull 2 ndash gradual movement forward

bull 3 ndash rest

bull 4 ndash backward movement

bull 5 ndash rest

1

2

3

4

5

T

D

Velocity Graphs and Profiles of Terrain

bull 1 ndash You are halfway up a hill at rest holding a wagon

bull 2 ndash You start moving uphillbull 3 ndash You take a restbull 4 ndash The wagon handle slips

out of you hand and travels backward down the hill

bull 5 ndash The wagon stops moving at the bottom of the hill

1

2

3

4

5

T

D

bull What could be a possible explanation pulling a wagon uphill

Dimensional Analysis ndash Unit Analysis

In your head you can probably converthellip

hellip inches to feet

sure 12 in = 1 ft

hellip inches to yards

okay 3 ft in 1 yd = 36 in

hellip inches to miles

um probably not

bull FAQ When I convert from inches to yards or yards to inches when do I multiply and when do I divide

bull The easiest way to approach these unit conversions is by using dimensional analysis

There are 4 rules1 If you use only one unit to start put it over a

12 Determine the conversion factors (Ex 12

inches = 1 ft) and put into a fraction3 Properly place the conversion factors in an

equation4 Check cancellations of units so that you are

left with the unit you were looking for on the top of a division bar The units that are canceled should be on opposite sides of the division bar

Example 1 How many feet in 13 in 1 112 or 1083 ftStep 1hellip starting with 13 sohellip 13 inches

1

Step 2hellip conversion factors 1 foot or 12 inches 12 inches 1 foot

Step 3hellip place factors 13 inches x 1 foot 1 12 inches

Step 4hellip check cancellations 13 inches x 1 foot 1 12

inches

13 inches = 1083 ft

Example 2 Convert 13 inches into yards

Step 1hellip starting with 13 sohellip 13 in

1

Step 2hellip conversion factors 1 ft 1 yd

12 in 3 ft

Step 3hellip place factors 13 in x 1 ft x 1 yd =

1 12 in 3 ft

Step 4hellip check cancellations 13 in x 1 ft x 1 yd

1 12 in 3 ft

13 in = 036 yd

Example 3 Convert 2 years into seconds

2 yrs x 365 days x 24 h x 60 min x 60 sec

1 1 yr 1 day 1 h 1 min

2 yrs = 63072000 sec

Example 4 Convert 4 decades into minutes

4 dec x 10 yrs x 365 days x 24 h x 60 min

1 1 dec 1 yr 1 day 1 h

4 decades = 21024000 m

Example 5 I am 5rsquo 3rdquo or (5 x 12) + 3 = 63 inches tall How many cm tall am I

63 in x 256 cm =

1 1 in

63 in = 1601 cm

Dimensional Analysis Worksheet

1 In New Jersey students in public schools go to school for 4 years How many minutes are students enrolled in high school

4 years x 365 days x 24 h x 60 min

1 1 yr 1 day 1 h

4 yrs = 2102400 min

2 Alaynarsquos dog is 3 ft tall What is the dogrsquos height in mm

3 ft x 12 in x 254 cm x 10 mm

1 1 ft 1 in 1 cm

3 ft = 9144 mm

3 Brian and Jesse were on a bus trip going 50 MPH For some extra fun they decided to convert the busrsquos speed into kmh What should their answer be

50 miles x 161 km 1 hr 1 mile

50 MPH = 805 kmh

4 Driving home from practice Alexrsquos mother was driving at a speed of 30 ms What was their speed in kmh

30 m x 1 km x 60 s x 60 min 1 s 1000 m 1 min 1 h

30 ms = 108 kmh

5 Saskia was riding her bike down the road at a speed of 5 kmh What was her speed in ms

5 km x 1000 m x 1 hr x 1 min 1 h 1 km 60 min 60 s

5 kmh = 139 ms

Class experiment

1 Determine how tall you are in inches

2 Using the conversion factor 1 mile = 161 km determine how tall you are in cm

3 Check your answer with a meter stick

AccelerationWhen you accelerate what are you doing

Speeding uphellip accelerating

When you slow down what are you doing

Decelerating

In physics we use the same term ldquoaccelerationrdquo for both speeding up and slowing down We distinguish between the two by assigning positive or negative values

+ acceleration as in speeding up positive

- acceleration as in slowing down negative

Acceleration = the change in velocity over time

- measured in ms or ms2

s

Acceleration = ∆ Velocity

∆ Time

Acceleration = ∆ Distance + Direction

∆ Time

∆ Time

Given an object moving in a circle

- ∆ velocity due to a ∆ direction

- if ∆ velocity the ∆ acceleration as well

- circular motion = ∆ D = ∆ V = ∆ A

Graphing Acceleration

A = ∆ V and slope = ∆ Y

∆ T ∆ X

Acceleration = ∆ V = ∆ Y = Slope of line

∆ T ∆ X

So Acceleration = Slope of line

Steep slope = fast movement

Gradual slope = slow movement

Acceleration Deceleration

V

T

V

T

Steepness of the line indicates the degree of acceleration

V

T

V

T

Comparing Velocity and Acceleration

Velocity = ∆ Distance Acceleration = ∆ Velocity

∆ Time ∆ Time

D

T

These two lines indicate the exact same thing the same rate of acceleration

bull Acceleration = + slope

bull Deceleration = - slope

T

V

+ slope

- slope

When object is a rest Velocity is zero

If ∆ Distance = 0 then ∆ Velocityhellip so Acceleration = 0

D

T

V

T

0

When acceleration equals zero

A= ∆ V no change in velocity

∆ T Time will always pass

No change in velocity

- no velocity ndash V = 0 then object is at rest

- constant velocity - ∆ V = Vfinal ndash Vinitial

Vf = 50 milesh and Vi = 50 milesh

Then ∆ V = 0

If acceleration = zero you are either stopped or on cruise control

To determine which you must find if there is a change in distance

How it all fits togetherFrom Motion Acceleration only one variable is

added at a time1 Motion = ∆ Distance2 Speed = ∆ Distance

∆ Time3 Velocity = ∆ Distance + Direction

∆ Time4 Acceleration = ∆ Distance + Direction

∆ Time∆ Time

Momentum

When an object is in motion we think velocity However we must not forget Momentum ndash which is also acting on the object

Momentum = a quantity defined as the product of an objectrsquos mass and its velocity - In a formula P = momentum- momentum moves in the same direction as the velocity

P = Mass x Velocity

- Measured in kgms

Momentum and ∆ Velocity

- large momentum difficult to change velocity

- small momentum easier to change velocity

Class Experiment Red light green light

Stationary objects have momentum of zero

Why No motion = no speed = no velocity = no momentum

Momentum is directly proportional to masshellip momentum increases as mass increases

P

Mass (kg)

Force

Force = the cause of acceleration or a change in velocity

- force is measured in units called Newtons

Net force = the combination of all the forces acting upon an object

bull The size of the arrow represents the amount of forcehellip

bull The arrows are the same so there is no movement

Friction

Friction = the force between two objects in contact that opposes the motion of either object

Pretend you are in a helicopter looking down on a ski slope in early springhellip The ice is meltinghellip Patches of dirt and gravel begin to showhellip

How much friction

Skis + snow = little frictionhellip skis move over snow

Skis + dirt = a lot of frictionhellip skis do not move over dirt

Air resistance is a type of friction

Gravity

Gravity = Force of attraction between 2 objects due to their masses

The force of gravity is different on different planets moons etc

On earth g = 98ms2

Gravity depends upon the masses as well as the distance between objects

Newtonrsquos Laws of Motion

Newtonrsquos 1st Law- the law of inertia

An object at rest remains at rest and an object in motion remains in motion unless it experiences an unbalanced force

bull Example 1 Whiplash ndash Person B is stopped at a traffic light Person A is not paying attention and rear-ends Person B

bull Result Person B moves forward suddenlyhellip Their head snaps back as it attempts to ldquoremain at restrdquo Their body attached to the seat moves forwardhellip their head snaps forward to catch up with the body resulting in whiplash

Example 2 Bus ride - The bus driver does not like children Every time they get too loud he slams on the breaks Why does he do this

Inertia = The tendency of an object to remain at rest or in motion with a constant velocity All objects have inertia because they resist changes in motion

Trivia If two people on a space ship (in space) get into a physical fight which will win

Person A Person B

Even though they are weightlesshellip there is no gravity Person A has a greater mass therefore a greater inertia

Newtonrsquos 2nd law of Motion- the law of acceleration

bull The unbalanced force acting on an object equals the objectrsquos mass times its acceleration

bull Force = Mass x Acceleration

Example pushing a cart

The greater the mass the more force needed to cause acceleration

Bumper cars

Image for remembering equations for speed math problems

VelocityVelocity = Speed and direction

ndashMeasured by a speedometer and a compass

bull Velocity = ∆ Distance + direction of movement

∆ Timebull In this class we will use the terms

interchangeablyhellip and imply the directionbull However

CONSTANT SPEED ne CONSTANT VELOCITY

The car can be traveling at the same speed but has changes in direction

bull Changes in velocity can have different causes

ndash ∆ V = same speed + ∆ direction

ndash ∆ V = ∆ speed + same direction

ndash ∆ V = ∆ speed + ∆ direction

Mathematical ndash Graphic Representations of Velocity

bull If we know the average speed we can plot the time and distance along a trip

Distances Traveled (miles)

Time (hours)

Car A at

15 MPH

Car B at

30 MPH

Car C at

60 MPH

05 75 15 30

1 15 30 60

15 225 45 90

2 30 60 120

Car Speed

0

20

40

60

80

100

120

140

0 05 1 15 2 25

Time (hours)

Dis

t m

iles

Car A

Car B

Car C

bull What do you notice about the 3 lines on the Car Speed graph

ndashSteepness of line = greater the slope of the line

ndashthe greater the slope the faster the speed of the car

ndash slope = ∆ Y or rise

∆ X run

ndash If distance is placed on the y-axis and time is placed on the x-axis

Velocity = ∆ D = ∆ Y = Slope of line

∆ T ∆ X

bull So Velocity = Slope of line

Car A Slow Gradual line

Car B Medium Medium

Car C Fast Steep line

Graphing Velocity (Average Speed)

What can you tell from different graphs

bull 3 Different objects moving at 3 different speeds

T

D

bull Stopped Object Time passes but distance does not change

bull No movement T

D

bull Backward moving objecthellip

bull The distance is decreasing so there is movement towards the source

T

D

bull Circular Motion Time passes as the same distances are revisited like a race track

T

D

bull Series of motions

bull Rest-forward-rest-backward-rest

bull Note does not represent the profile of the terrain

T

D

Velocity Graphs and Profiles of Terrain

bull What do we know about movement

bull 1 ndash rest

bull 2 ndash gradual movement forward

bull 3 ndash rest

bull 4 ndash backward movement

bull 5 ndash rest

1

2

3

4

5

T

D

Velocity Graphs and Profiles of Terrain

bull 1 ndash You are halfway up a hill at rest holding a wagon

bull 2 ndash You start moving uphillbull 3 ndash You take a restbull 4 ndash The wagon handle slips

out of you hand and travels backward down the hill

bull 5 ndash The wagon stops moving at the bottom of the hill

1

2

3

4

5

T

D

bull What could be a possible explanation pulling a wagon uphill

Dimensional Analysis ndash Unit Analysis

In your head you can probably converthellip

hellip inches to feet

sure 12 in = 1 ft

hellip inches to yards

okay 3 ft in 1 yd = 36 in

hellip inches to miles

um probably not

bull FAQ When I convert from inches to yards or yards to inches when do I multiply and when do I divide

bull The easiest way to approach these unit conversions is by using dimensional analysis

There are 4 rules1 If you use only one unit to start put it over a

12 Determine the conversion factors (Ex 12

inches = 1 ft) and put into a fraction3 Properly place the conversion factors in an

equation4 Check cancellations of units so that you are

left with the unit you were looking for on the top of a division bar The units that are canceled should be on opposite sides of the division bar

Example 1 How many feet in 13 in 1 112 or 1083 ftStep 1hellip starting with 13 sohellip 13 inches

1

Step 2hellip conversion factors 1 foot or 12 inches 12 inches 1 foot

Step 3hellip place factors 13 inches x 1 foot 1 12 inches

Step 4hellip check cancellations 13 inches x 1 foot 1 12

inches

13 inches = 1083 ft

Example 2 Convert 13 inches into yards

Step 1hellip starting with 13 sohellip 13 in

1

Step 2hellip conversion factors 1 ft 1 yd

12 in 3 ft

Step 3hellip place factors 13 in x 1 ft x 1 yd =

1 12 in 3 ft

Step 4hellip check cancellations 13 in x 1 ft x 1 yd

1 12 in 3 ft

13 in = 036 yd

Example 3 Convert 2 years into seconds

2 yrs x 365 days x 24 h x 60 min x 60 sec

1 1 yr 1 day 1 h 1 min

2 yrs = 63072000 sec

Example 4 Convert 4 decades into minutes

4 dec x 10 yrs x 365 days x 24 h x 60 min

1 1 dec 1 yr 1 day 1 h

4 decades = 21024000 m

Example 5 I am 5rsquo 3rdquo or (5 x 12) + 3 = 63 inches tall How many cm tall am I

63 in x 256 cm =

1 1 in

63 in = 1601 cm

Dimensional Analysis Worksheet

1 In New Jersey students in public schools go to school for 4 years How many minutes are students enrolled in high school

4 years x 365 days x 24 h x 60 min

1 1 yr 1 day 1 h

4 yrs = 2102400 min

2 Alaynarsquos dog is 3 ft tall What is the dogrsquos height in mm

3 ft x 12 in x 254 cm x 10 mm

1 1 ft 1 in 1 cm

3 ft = 9144 mm

3 Brian and Jesse were on a bus trip going 50 MPH For some extra fun they decided to convert the busrsquos speed into kmh What should their answer be

50 miles x 161 km 1 hr 1 mile

50 MPH = 805 kmh

4 Driving home from practice Alexrsquos mother was driving at a speed of 30 ms What was their speed in kmh

30 m x 1 km x 60 s x 60 min 1 s 1000 m 1 min 1 h

30 ms = 108 kmh

5 Saskia was riding her bike down the road at a speed of 5 kmh What was her speed in ms

5 km x 1000 m x 1 hr x 1 min 1 h 1 km 60 min 60 s

5 kmh = 139 ms

Class experiment

1 Determine how tall you are in inches

2 Using the conversion factor 1 mile = 161 km determine how tall you are in cm

3 Check your answer with a meter stick

AccelerationWhen you accelerate what are you doing

Speeding uphellip accelerating

When you slow down what are you doing

Decelerating

In physics we use the same term ldquoaccelerationrdquo for both speeding up and slowing down We distinguish between the two by assigning positive or negative values

+ acceleration as in speeding up positive

- acceleration as in slowing down negative

Acceleration = the change in velocity over time

- measured in ms or ms2

s

Acceleration = ∆ Velocity

∆ Time

Acceleration = ∆ Distance + Direction

∆ Time

∆ Time

Given an object moving in a circle

- ∆ velocity due to a ∆ direction

- if ∆ velocity the ∆ acceleration as well

- circular motion = ∆ D = ∆ V = ∆ A

Graphing Acceleration

A = ∆ V and slope = ∆ Y

∆ T ∆ X

Acceleration = ∆ V = ∆ Y = Slope of line

∆ T ∆ X

So Acceleration = Slope of line

Steep slope = fast movement

Gradual slope = slow movement

Acceleration Deceleration

V

T

V

T

Steepness of the line indicates the degree of acceleration

V

T

V

T

Comparing Velocity and Acceleration

Velocity = ∆ Distance Acceleration = ∆ Velocity

∆ Time ∆ Time

D

T

These two lines indicate the exact same thing the same rate of acceleration

bull Acceleration = + slope

bull Deceleration = - slope

T

V

+ slope

- slope

When object is a rest Velocity is zero

If ∆ Distance = 0 then ∆ Velocityhellip so Acceleration = 0

D

T

V

T

0

When acceleration equals zero

A= ∆ V no change in velocity

∆ T Time will always pass

No change in velocity

- no velocity ndash V = 0 then object is at rest

- constant velocity - ∆ V = Vfinal ndash Vinitial

Vf = 50 milesh and Vi = 50 milesh

Then ∆ V = 0

If acceleration = zero you are either stopped or on cruise control

To determine which you must find if there is a change in distance

How it all fits togetherFrom Motion Acceleration only one variable is

added at a time1 Motion = ∆ Distance2 Speed = ∆ Distance

∆ Time3 Velocity = ∆ Distance + Direction

∆ Time4 Acceleration = ∆ Distance + Direction

∆ Time∆ Time

Momentum

When an object is in motion we think velocity However we must not forget Momentum ndash which is also acting on the object

Momentum = a quantity defined as the product of an objectrsquos mass and its velocity - In a formula P = momentum- momentum moves in the same direction as the velocity

P = Mass x Velocity

- Measured in kgms

Momentum and ∆ Velocity

- large momentum difficult to change velocity

- small momentum easier to change velocity

Class Experiment Red light green light

Stationary objects have momentum of zero

Why No motion = no speed = no velocity = no momentum

Momentum is directly proportional to masshellip momentum increases as mass increases

P

Mass (kg)

Force

Force = the cause of acceleration or a change in velocity

- force is measured in units called Newtons

Net force = the combination of all the forces acting upon an object

bull The size of the arrow represents the amount of forcehellip

bull The arrows are the same so there is no movement

Friction

Friction = the force between two objects in contact that opposes the motion of either object

Pretend you are in a helicopter looking down on a ski slope in early springhellip The ice is meltinghellip Patches of dirt and gravel begin to showhellip

How much friction

Skis + snow = little frictionhellip skis move over snow

Skis + dirt = a lot of frictionhellip skis do not move over dirt

Air resistance is a type of friction

Gravity

Gravity = Force of attraction between 2 objects due to their masses

The force of gravity is different on different planets moons etc

On earth g = 98ms2

Gravity depends upon the masses as well as the distance between objects

Newtonrsquos Laws of Motion

Newtonrsquos 1st Law- the law of inertia

An object at rest remains at rest and an object in motion remains in motion unless it experiences an unbalanced force

bull Example 1 Whiplash ndash Person B is stopped at a traffic light Person A is not paying attention and rear-ends Person B

bull Result Person B moves forward suddenlyhellip Their head snaps back as it attempts to ldquoremain at restrdquo Their body attached to the seat moves forwardhellip their head snaps forward to catch up with the body resulting in whiplash

Example 2 Bus ride - The bus driver does not like children Every time they get too loud he slams on the breaks Why does he do this

Inertia = The tendency of an object to remain at rest or in motion with a constant velocity All objects have inertia because they resist changes in motion

Trivia If two people on a space ship (in space) get into a physical fight which will win

Person A Person B

Even though they are weightlesshellip there is no gravity Person A has a greater mass therefore a greater inertia

Newtonrsquos 2nd law of Motion- the law of acceleration

bull The unbalanced force acting on an object equals the objectrsquos mass times its acceleration

bull Force = Mass x Acceleration

Example pushing a cart

The greater the mass the more force needed to cause acceleration

Bumper cars

VelocityVelocity = Speed and direction

ndashMeasured by a speedometer and a compass

bull Velocity = ∆ Distance + direction of movement

∆ Timebull In this class we will use the terms

interchangeablyhellip and imply the directionbull However

CONSTANT SPEED ne CONSTANT VELOCITY

The car can be traveling at the same speed but has changes in direction

bull Changes in velocity can have different causes

ndash ∆ V = same speed + ∆ direction

ndash ∆ V = ∆ speed + same direction

ndash ∆ V = ∆ speed + ∆ direction

Mathematical ndash Graphic Representations of Velocity

bull If we know the average speed we can plot the time and distance along a trip

Distances Traveled (miles)

Time (hours)

Car A at

15 MPH

Car B at

30 MPH

Car C at

60 MPH

05 75 15 30

1 15 30 60

15 225 45 90

2 30 60 120

Car Speed

0

20

40

60

80

100

120

140

0 05 1 15 2 25

Time (hours)

Dis

t m

iles

Car A

Car B

Car C

bull What do you notice about the 3 lines on the Car Speed graph

ndashSteepness of line = greater the slope of the line

ndashthe greater the slope the faster the speed of the car

ndash slope = ∆ Y or rise

∆ X run

ndash If distance is placed on the y-axis and time is placed on the x-axis

Velocity = ∆ D = ∆ Y = Slope of line

∆ T ∆ X

bull So Velocity = Slope of line

Car A Slow Gradual line

Car B Medium Medium

Car C Fast Steep line

Graphing Velocity (Average Speed)

What can you tell from different graphs

bull 3 Different objects moving at 3 different speeds

T

D

bull Stopped Object Time passes but distance does not change

bull No movement T

D

bull Backward moving objecthellip

bull The distance is decreasing so there is movement towards the source

T

D

bull Circular Motion Time passes as the same distances are revisited like a race track

T

D

bull Series of motions

bull Rest-forward-rest-backward-rest

bull Note does not represent the profile of the terrain

T

D

Velocity Graphs and Profiles of Terrain

bull What do we know about movement

bull 1 ndash rest

bull 2 ndash gradual movement forward

bull 3 ndash rest

bull 4 ndash backward movement

bull 5 ndash rest

1

2

3

4

5

T

D

Velocity Graphs and Profiles of Terrain

bull 1 ndash You are halfway up a hill at rest holding a wagon

bull 2 ndash You start moving uphillbull 3 ndash You take a restbull 4 ndash The wagon handle slips

out of you hand and travels backward down the hill

bull 5 ndash The wagon stops moving at the bottom of the hill

1

2

3

4

5

T

D

bull What could be a possible explanation pulling a wagon uphill

Dimensional Analysis ndash Unit Analysis

In your head you can probably converthellip

hellip inches to feet

sure 12 in = 1 ft

hellip inches to yards

okay 3 ft in 1 yd = 36 in

hellip inches to miles

um probably not

bull FAQ When I convert from inches to yards or yards to inches when do I multiply and when do I divide

bull The easiest way to approach these unit conversions is by using dimensional analysis

There are 4 rules1 If you use only one unit to start put it over a

12 Determine the conversion factors (Ex 12

inches = 1 ft) and put into a fraction3 Properly place the conversion factors in an

equation4 Check cancellations of units so that you are

left with the unit you were looking for on the top of a division bar The units that are canceled should be on opposite sides of the division bar

Example 1 How many feet in 13 in 1 112 or 1083 ftStep 1hellip starting with 13 sohellip 13 inches

1

Step 2hellip conversion factors 1 foot or 12 inches 12 inches 1 foot

Step 3hellip place factors 13 inches x 1 foot 1 12 inches

Step 4hellip check cancellations 13 inches x 1 foot 1 12

inches

13 inches = 1083 ft

Example 2 Convert 13 inches into yards

Step 1hellip starting with 13 sohellip 13 in

1

Step 2hellip conversion factors 1 ft 1 yd

12 in 3 ft

Step 3hellip place factors 13 in x 1 ft x 1 yd =

1 12 in 3 ft

Step 4hellip check cancellations 13 in x 1 ft x 1 yd

1 12 in 3 ft

13 in = 036 yd

Example 3 Convert 2 years into seconds

2 yrs x 365 days x 24 h x 60 min x 60 sec

1 1 yr 1 day 1 h 1 min

2 yrs = 63072000 sec

Example 4 Convert 4 decades into minutes

4 dec x 10 yrs x 365 days x 24 h x 60 min

1 1 dec 1 yr 1 day 1 h

4 decades = 21024000 m

Example 5 I am 5rsquo 3rdquo or (5 x 12) + 3 = 63 inches tall How many cm tall am I

63 in x 256 cm =

1 1 in

63 in = 1601 cm

Dimensional Analysis Worksheet

1 In New Jersey students in public schools go to school for 4 years How many minutes are students enrolled in high school

4 years x 365 days x 24 h x 60 min

1 1 yr 1 day 1 h

4 yrs = 2102400 min

2 Alaynarsquos dog is 3 ft tall What is the dogrsquos height in mm

3 ft x 12 in x 254 cm x 10 mm

1 1 ft 1 in 1 cm

3 ft = 9144 mm

3 Brian and Jesse were on a bus trip going 50 MPH For some extra fun they decided to convert the busrsquos speed into kmh What should their answer be

50 miles x 161 km 1 hr 1 mile

50 MPH = 805 kmh

4 Driving home from practice Alexrsquos mother was driving at a speed of 30 ms What was their speed in kmh

30 m x 1 km x 60 s x 60 min 1 s 1000 m 1 min 1 h

30 ms = 108 kmh

5 Saskia was riding her bike down the road at a speed of 5 kmh What was her speed in ms

5 km x 1000 m x 1 hr x 1 min 1 h 1 km 60 min 60 s

5 kmh = 139 ms

Class experiment

1 Determine how tall you are in inches

2 Using the conversion factor 1 mile = 161 km determine how tall you are in cm

3 Check your answer with a meter stick

AccelerationWhen you accelerate what are you doing

Speeding uphellip accelerating

When you slow down what are you doing

Decelerating

In physics we use the same term ldquoaccelerationrdquo for both speeding up and slowing down We distinguish between the two by assigning positive or negative values

+ acceleration as in speeding up positive

- acceleration as in slowing down negative

Acceleration = the change in velocity over time

- measured in ms or ms2

s

Acceleration = ∆ Velocity

∆ Time

Acceleration = ∆ Distance + Direction

∆ Time

∆ Time

Given an object moving in a circle

- ∆ velocity due to a ∆ direction

- if ∆ velocity the ∆ acceleration as well

- circular motion = ∆ D = ∆ V = ∆ A

Graphing Acceleration

A = ∆ V and slope = ∆ Y

∆ T ∆ X

Acceleration = ∆ V = ∆ Y = Slope of line

∆ T ∆ X

So Acceleration = Slope of line

Steep slope = fast movement

Gradual slope = slow movement

Acceleration Deceleration

V

T

V

T

Steepness of the line indicates the degree of acceleration

V

T

V

T

Comparing Velocity and Acceleration

Velocity = ∆ Distance Acceleration = ∆ Velocity

∆ Time ∆ Time

D

T

These two lines indicate the exact same thing the same rate of acceleration

bull Acceleration = + slope

bull Deceleration = - slope

T

V

+ slope

- slope

When object is a rest Velocity is zero

If ∆ Distance = 0 then ∆ Velocityhellip so Acceleration = 0

D

T

V

T

0

When acceleration equals zero

A= ∆ V no change in velocity

∆ T Time will always pass

No change in velocity

- no velocity ndash V = 0 then object is at rest

- constant velocity - ∆ V = Vfinal ndash Vinitial

Vf = 50 milesh and Vi = 50 milesh

Then ∆ V = 0

If acceleration = zero you are either stopped or on cruise control

To determine which you must find if there is a change in distance

How it all fits togetherFrom Motion Acceleration only one variable is

added at a time1 Motion = ∆ Distance2 Speed = ∆ Distance

∆ Time3 Velocity = ∆ Distance + Direction

∆ Time4 Acceleration = ∆ Distance + Direction

∆ Time∆ Time

Momentum

When an object is in motion we think velocity However we must not forget Momentum ndash which is also acting on the object

Momentum = a quantity defined as the product of an objectrsquos mass and its velocity - In a formula P = momentum- momentum moves in the same direction as the velocity

P = Mass x Velocity

- Measured in kgms

Momentum and ∆ Velocity

- large momentum difficult to change velocity

- small momentum easier to change velocity

Class Experiment Red light green light

Stationary objects have momentum of zero

Why No motion = no speed = no velocity = no momentum

Momentum is directly proportional to masshellip momentum increases as mass increases

P

Mass (kg)

Force

Force = the cause of acceleration or a change in velocity

- force is measured in units called Newtons

Net force = the combination of all the forces acting upon an object

bull The size of the arrow represents the amount of forcehellip

bull The arrows are the same so there is no movement

Friction

Friction = the force between two objects in contact that opposes the motion of either object

Pretend you are in a helicopter looking down on a ski slope in early springhellip The ice is meltinghellip Patches of dirt and gravel begin to showhellip

How much friction

Skis + snow = little frictionhellip skis move over snow

Skis + dirt = a lot of frictionhellip skis do not move over dirt

Air resistance is a type of friction

Gravity

Gravity = Force of attraction between 2 objects due to their masses

The force of gravity is different on different planets moons etc

On earth g = 98ms2

Gravity depends upon the masses as well as the distance between objects

Newtonrsquos Laws of Motion

Newtonrsquos 1st Law- the law of inertia

An object at rest remains at rest and an object in motion remains in motion unless it experiences an unbalanced force

bull Example 1 Whiplash ndash Person B is stopped at a traffic light Person A is not paying attention and rear-ends Person B

bull Result Person B moves forward suddenlyhellip Their head snaps back as it attempts to ldquoremain at restrdquo Their body attached to the seat moves forwardhellip their head snaps forward to catch up with the body resulting in whiplash

Example 2 Bus ride - The bus driver does not like children Every time they get too loud he slams on the breaks Why does he do this

Inertia = The tendency of an object to remain at rest or in motion with a constant velocity All objects have inertia because they resist changes in motion

Trivia If two people on a space ship (in space) get into a physical fight which will win

Person A Person B

Even though they are weightlesshellip there is no gravity Person A has a greater mass therefore a greater inertia

Newtonrsquos 2nd law of Motion- the law of acceleration

bull The unbalanced force acting on an object equals the objectrsquos mass times its acceleration

bull Force = Mass x Acceleration

Example pushing a cart

The greater the mass the more force needed to cause acceleration

Bumper cars

The car can be traveling at the same speed but has changes in direction

bull Changes in velocity can have different causes

ndash ∆ V = same speed + ∆ direction

ndash ∆ V = ∆ speed + same direction

ndash ∆ V = ∆ speed + ∆ direction

Mathematical ndash Graphic Representations of Velocity

bull If we know the average speed we can plot the time and distance along a trip

Distances Traveled (miles)

Time (hours)

Car A at

15 MPH

Car B at

30 MPH

Car C at

60 MPH

05 75 15 30

1 15 30 60

15 225 45 90

2 30 60 120

Car Speed

0

20

40

60

80

100

120

140

0 05 1 15 2 25

Time (hours)

Dis

t m

iles

Car A

Car B

Car C

bull What do you notice about the 3 lines on the Car Speed graph

ndashSteepness of line = greater the slope of the line

ndashthe greater the slope the faster the speed of the car

ndash slope = ∆ Y or rise

∆ X run

ndash If distance is placed on the y-axis and time is placed on the x-axis

Velocity = ∆ D = ∆ Y = Slope of line

∆ T ∆ X

bull So Velocity = Slope of line

Car A Slow Gradual line

Car B Medium Medium

Car C Fast Steep line

Graphing Velocity (Average Speed)

What can you tell from different graphs

bull 3 Different objects moving at 3 different speeds

T

D

bull Stopped Object Time passes but distance does not change

bull No movement T

D

bull Backward moving objecthellip

bull The distance is decreasing so there is movement towards the source

T

D

bull Circular Motion Time passes as the same distances are revisited like a race track

T

D

bull Series of motions

bull Rest-forward-rest-backward-rest

bull Note does not represent the profile of the terrain

T

D

Velocity Graphs and Profiles of Terrain

bull What do we know about movement

bull 1 ndash rest

bull 2 ndash gradual movement forward

bull 3 ndash rest

bull 4 ndash backward movement

bull 5 ndash rest

1

2

3

4

5

T

D

Velocity Graphs and Profiles of Terrain

bull 1 ndash You are halfway up a hill at rest holding a wagon

bull 2 ndash You start moving uphillbull 3 ndash You take a restbull 4 ndash The wagon handle slips

out of you hand and travels backward down the hill

bull 5 ndash The wagon stops moving at the bottom of the hill

1

2

3

4

5

T

D

bull What could be a possible explanation pulling a wagon uphill

Dimensional Analysis ndash Unit Analysis

In your head you can probably converthellip

hellip inches to feet

sure 12 in = 1 ft

hellip inches to yards

okay 3 ft in 1 yd = 36 in

hellip inches to miles

um probably not

bull FAQ When I convert from inches to yards or yards to inches when do I multiply and when do I divide

bull The easiest way to approach these unit conversions is by using dimensional analysis

There are 4 rules1 If you use only one unit to start put it over a

12 Determine the conversion factors (Ex 12

inches = 1 ft) and put into a fraction3 Properly place the conversion factors in an

equation4 Check cancellations of units so that you are

left with the unit you were looking for on the top of a division bar The units that are canceled should be on opposite sides of the division bar

Example 1 How many feet in 13 in 1 112 or 1083 ftStep 1hellip starting with 13 sohellip 13 inches

1

Step 2hellip conversion factors 1 foot or 12 inches 12 inches 1 foot

Step 3hellip place factors 13 inches x 1 foot 1 12 inches

Step 4hellip check cancellations 13 inches x 1 foot 1 12

inches

13 inches = 1083 ft

Example 2 Convert 13 inches into yards

Step 1hellip starting with 13 sohellip 13 in

1

Step 2hellip conversion factors 1 ft 1 yd

12 in 3 ft

Step 3hellip place factors 13 in x 1 ft x 1 yd =

1 12 in 3 ft

Step 4hellip check cancellations 13 in x 1 ft x 1 yd

1 12 in 3 ft

13 in = 036 yd

Example 3 Convert 2 years into seconds

2 yrs x 365 days x 24 h x 60 min x 60 sec

1 1 yr 1 day 1 h 1 min

2 yrs = 63072000 sec

Example 4 Convert 4 decades into minutes

4 dec x 10 yrs x 365 days x 24 h x 60 min

1 1 dec 1 yr 1 day 1 h

4 decades = 21024000 m

Example 5 I am 5rsquo 3rdquo or (5 x 12) + 3 = 63 inches tall How many cm tall am I

63 in x 256 cm =

1 1 in

63 in = 1601 cm

Dimensional Analysis Worksheet

1 In New Jersey students in public schools go to school for 4 years How many minutes are students enrolled in high school

4 years x 365 days x 24 h x 60 min

1 1 yr 1 day 1 h

4 yrs = 2102400 min

2 Alaynarsquos dog is 3 ft tall What is the dogrsquos height in mm

3 ft x 12 in x 254 cm x 10 mm

1 1 ft 1 in 1 cm

3 ft = 9144 mm

3 Brian and Jesse were on a bus trip going 50 MPH For some extra fun they decided to convert the busrsquos speed into kmh What should their answer be

50 miles x 161 km 1 hr 1 mile

50 MPH = 805 kmh

4 Driving home from practice Alexrsquos mother was driving at a speed of 30 ms What was their speed in kmh

30 m x 1 km x 60 s x 60 min 1 s 1000 m 1 min 1 h

30 ms = 108 kmh

5 Saskia was riding her bike down the road at a speed of 5 kmh What was her speed in ms

5 km x 1000 m x 1 hr x 1 min 1 h 1 km 60 min 60 s

5 kmh = 139 ms

Class experiment

1 Determine how tall you are in inches

2 Using the conversion factor 1 mile = 161 km determine how tall you are in cm

3 Check your answer with a meter stick

AccelerationWhen you accelerate what are you doing

Speeding uphellip accelerating

When you slow down what are you doing

Decelerating

In physics we use the same term ldquoaccelerationrdquo for both speeding up and slowing down We distinguish between the two by assigning positive or negative values

+ acceleration as in speeding up positive

- acceleration as in slowing down negative

Acceleration = the change in velocity over time

- measured in ms or ms2

s

Acceleration = ∆ Velocity

∆ Time

Acceleration = ∆ Distance + Direction

∆ Time

∆ Time

Given an object moving in a circle

- ∆ velocity due to a ∆ direction

- if ∆ velocity the ∆ acceleration as well

- circular motion = ∆ D = ∆ V = ∆ A

Graphing Acceleration

A = ∆ V and slope = ∆ Y

∆ T ∆ X

Acceleration = ∆ V = ∆ Y = Slope of line

∆ T ∆ X

So Acceleration = Slope of line

Steep slope = fast movement

Gradual slope = slow movement

Acceleration Deceleration

V

T

V

T

Steepness of the line indicates the degree of acceleration

V

T

V

T

Comparing Velocity and Acceleration

Velocity = ∆ Distance Acceleration = ∆ Velocity

∆ Time ∆ Time

D

T

These two lines indicate the exact same thing the same rate of acceleration

bull Acceleration = + slope

bull Deceleration = - slope

T

V

+ slope

- slope

When object is a rest Velocity is zero

If ∆ Distance = 0 then ∆ Velocityhellip so Acceleration = 0

D

T

V

T

0

When acceleration equals zero

A= ∆ V no change in velocity

∆ T Time will always pass

No change in velocity

- no velocity ndash V = 0 then object is at rest

- constant velocity - ∆ V = Vfinal ndash Vinitial

Vf = 50 milesh and Vi = 50 milesh

Then ∆ V = 0

If acceleration = zero you are either stopped or on cruise control

To determine which you must find if there is a change in distance

How it all fits togetherFrom Motion Acceleration only one variable is

added at a time1 Motion = ∆ Distance2 Speed = ∆ Distance

∆ Time3 Velocity = ∆ Distance + Direction

∆ Time4 Acceleration = ∆ Distance + Direction

∆ Time∆ Time

Momentum

When an object is in motion we think velocity However we must not forget Momentum ndash which is also acting on the object

Momentum = a quantity defined as the product of an objectrsquos mass and its velocity - In a formula P = momentum- momentum moves in the same direction as the velocity

P = Mass x Velocity

- Measured in kgms

Momentum and ∆ Velocity

- large momentum difficult to change velocity

- small momentum easier to change velocity

Class Experiment Red light green light

Stationary objects have momentum of zero

Why No motion = no speed = no velocity = no momentum

Momentum is directly proportional to masshellip momentum increases as mass increases

P

Mass (kg)

Force

Force = the cause of acceleration or a change in velocity

- force is measured in units called Newtons

Net force = the combination of all the forces acting upon an object

bull The size of the arrow represents the amount of forcehellip

bull The arrows are the same so there is no movement

Friction

Friction = the force between two objects in contact that opposes the motion of either object

Pretend you are in a helicopter looking down on a ski slope in early springhellip The ice is meltinghellip Patches of dirt and gravel begin to showhellip

How much friction

Skis + snow = little frictionhellip skis move over snow

Skis + dirt = a lot of frictionhellip skis do not move over dirt

Air resistance is a type of friction

Gravity

Gravity = Force of attraction between 2 objects due to their masses

The force of gravity is different on different planets moons etc

On earth g = 98ms2

Gravity depends upon the masses as well as the distance between objects

Newtonrsquos Laws of Motion

Newtonrsquos 1st Law- the law of inertia

An object at rest remains at rest and an object in motion remains in motion unless it experiences an unbalanced force

bull Example 1 Whiplash ndash Person B is stopped at a traffic light Person A is not paying attention and rear-ends Person B

bull Result Person B moves forward suddenlyhellip Their head snaps back as it attempts to ldquoremain at restrdquo Their body attached to the seat moves forwardhellip their head snaps forward to catch up with the body resulting in whiplash

Example 2 Bus ride - The bus driver does not like children Every time they get too loud he slams on the breaks Why does he do this

Inertia = The tendency of an object to remain at rest or in motion with a constant velocity All objects have inertia because they resist changes in motion

Trivia If two people on a space ship (in space) get into a physical fight which will win

Person A Person B

Even though they are weightlesshellip there is no gravity Person A has a greater mass therefore a greater inertia

Newtonrsquos 2nd law of Motion- the law of acceleration

bull The unbalanced force acting on an object equals the objectrsquos mass times its acceleration

bull Force = Mass x Acceleration

Example pushing a cart

The greater the mass the more force needed to cause acceleration

Bumper cars

Mathematical ndash Graphic Representations of Velocity

bull If we know the average speed we can plot the time and distance along a trip

Distances Traveled (miles)

Time (hours)

Car A at

15 MPH

Car B at

30 MPH

Car C at

60 MPH

05 75 15 30

1 15 30 60

15 225 45 90

2 30 60 120

Car Speed

0

20

40

60

80

100

120

140

0 05 1 15 2 25

Time (hours)

Dis

t m

iles

Car A

Car B

Car C

bull What do you notice about the 3 lines on the Car Speed graph

ndashSteepness of line = greater the slope of the line

ndashthe greater the slope the faster the speed of the car

ndash slope = ∆ Y or rise

∆ X run

ndash If distance is placed on the y-axis and time is placed on the x-axis

Velocity = ∆ D = ∆ Y = Slope of line

∆ T ∆ X

bull So Velocity = Slope of line

Car A Slow Gradual line

Car B Medium Medium

Car C Fast Steep line

Graphing Velocity (Average Speed)

What can you tell from different graphs

bull 3 Different objects moving at 3 different speeds

T

D

bull Stopped Object Time passes but distance does not change

bull No movement T

D

bull Backward moving objecthellip

bull The distance is decreasing so there is movement towards the source

T

D

bull Circular Motion Time passes as the same distances are revisited like a race track

T

D

bull Series of motions

bull Rest-forward-rest-backward-rest

bull Note does not represent the profile of the terrain

T

D

Velocity Graphs and Profiles of Terrain

bull What do we know about movement

bull 1 ndash rest

bull 2 ndash gradual movement forward

bull 3 ndash rest

bull 4 ndash backward movement

bull 5 ndash rest

1

2

3

4

5

T

D

Velocity Graphs and Profiles of Terrain

bull 1 ndash You are halfway up a hill at rest holding a wagon

bull 2 ndash You start moving uphillbull 3 ndash You take a restbull 4 ndash The wagon handle slips

out of you hand and travels backward down the hill

bull 5 ndash The wagon stops moving at the bottom of the hill

1

2

3

4

5

T

D

bull What could be a possible explanation pulling a wagon uphill

Dimensional Analysis ndash Unit Analysis

In your head you can probably converthellip

hellip inches to feet

sure 12 in = 1 ft

hellip inches to yards

okay 3 ft in 1 yd = 36 in

hellip inches to miles

um probably not

bull FAQ When I convert from inches to yards or yards to inches when do I multiply and when do I divide

bull The easiest way to approach these unit conversions is by using dimensional analysis

There are 4 rules1 If you use only one unit to start put it over a

12 Determine the conversion factors (Ex 12

inches = 1 ft) and put into a fraction3 Properly place the conversion factors in an

equation4 Check cancellations of units so that you are

left with the unit you were looking for on the top of a division bar The units that are canceled should be on opposite sides of the division bar

Example 1 How many feet in 13 in 1 112 or 1083 ftStep 1hellip starting with 13 sohellip 13 inches

1

Step 2hellip conversion factors 1 foot or 12 inches 12 inches 1 foot

Step 3hellip place factors 13 inches x 1 foot 1 12 inches

Step 4hellip check cancellations 13 inches x 1 foot 1 12

inches

13 inches = 1083 ft

Example 2 Convert 13 inches into yards

Step 1hellip starting with 13 sohellip 13 in

1

Step 2hellip conversion factors 1 ft 1 yd

12 in 3 ft

Step 3hellip place factors 13 in x 1 ft x 1 yd =

1 12 in 3 ft

Step 4hellip check cancellations 13 in x 1 ft x 1 yd

1 12 in 3 ft

13 in = 036 yd

Example 3 Convert 2 years into seconds

2 yrs x 365 days x 24 h x 60 min x 60 sec

1 1 yr 1 day 1 h 1 min

2 yrs = 63072000 sec

Example 4 Convert 4 decades into minutes

4 dec x 10 yrs x 365 days x 24 h x 60 min

1 1 dec 1 yr 1 day 1 h

4 decades = 21024000 m

Example 5 I am 5rsquo 3rdquo or (5 x 12) + 3 = 63 inches tall How many cm tall am I

63 in x 256 cm =

1 1 in

63 in = 1601 cm

Dimensional Analysis Worksheet

1 In New Jersey students in public schools go to school for 4 years How many minutes are students enrolled in high school

4 years x 365 days x 24 h x 60 min

1 1 yr 1 day 1 h

4 yrs = 2102400 min

2 Alaynarsquos dog is 3 ft tall What is the dogrsquos height in mm

3 ft x 12 in x 254 cm x 10 mm

1 1 ft 1 in 1 cm

3 ft = 9144 mm

3 Brian and Jesse were on a bus trip going 50 MPH For some extra fun they decided to convert the busrsquos speed into kmh What should their answer be

50 miles x 161 km 1 hr 1 mile

50 MPH = 805 kmh

4 Driving home from practice Alexrsquos mother was driving at a speed of 30 ms What was their speed in kmh

30 m x 1 km x 60 s x 60 min 1 s 1000 m 1 min 1 h

30 ms = 108 kmh

5 Saskia was riding her bike down the road at a speed of 5 kmh What was her speed in ms

5 km x 1000 m x 1 hr x 1 min 1 h 1 km 60 min 60 s

5 kmh = 139 ms

Class experiment

1 Determine how tall you are in inches

2 Using the conversion factor 1 mile = 161 km determine how tall you are in cm

3 Check your answer with a meter stick

AccelerationWhen you accelerate what are you doing

Speeding uphellip accelerating

When you slow down what are you doing

Decelerating

In physics we use the same term ldquoaccelerationrdquo for both speeding up and slowing down We distinguish between the two by assigning positive or negative values

+ acceleration as in speeding up positive

- acceleration as in slowing down negative

Acceleration = the change in velocity over time

- measured in ms or ms2

s

Acceleration = ∆ Velocity

∆ Time

Acceleration = ∆ Distance + Direction

∆ Time

∆ Time

Given an object moving in a circle

- ∆ velocity due to a ∆ direction

- if ∆ velocity the ∆ acceleration as well

- circular motion = ∆ D = ∆ V = ∆ A

Graphing Acceleration

A = ∆ V and slope = ∆ Y

∆ T ∆ X

Acceleration = ∆ V = ∆ Y = Slope of line

∆ T ∆ X

So Acceleration = Slope of line

Steep slope = fast movement

Gradual slope = slow movement

Acceleration Deceleration

V

T

V

T

Steepness of the line indicates the degree of acceleration

V

T

V

T

Comparing Velocity and Acceleration

Velocity = ∆ Distance Acceleration = ∆ Velocity

∆ Time ∆ Time

D

T

These two lines indicate the exact same thing the same rate of acceleration

bull Acceleration = + slope

bull Deceleration = - slope

T

V

+ slope

- slope

When object is a rest Velocity is zero

If ∆ Distance = 0 then ∆ Velocityhellip so Acceleration = 0

D

T

V

T

0

When acceleration equals zero

A= ∆ V no change in velocity

∆ T Time will always pass

No change in velocity

- no velocity ndash V = 0 then object is at rest

- constant velocity - ∆ V = Vfinal ndash Vinitial

Vf = 50 milesh and Vi = 50 milesh

Then ∆ V = 0

If acceleration = zero you are either stopped or on cruise control

To determine which you must find if there is a change in distance

How it all fits togetherFrom Motion Acceleration only one variable is

added at a time1 Motion = ∆ Distance2 Speed = ∆ Distance

∆ Time3 Velocity = ∆ Distance + Direction

∆ Time4 Acceleration = ∆ Distance + Direction

∆ Time∆ Time

Momentum

When an object is in motion we think velocity However we must not forget Momentum ndash which is also acting on the object

Momentum = a quantity defined as the product of an objectrsquos mass and its velocity - In a formula P = momentum- momentum moves in the same direction as the velocity

P = Mass x Velocity

- Measured in kgms

Momentum and ∆ Velocity

- large momentum difficult to change velocity

- small momentum easier to change velocity

Class Experiment Red light green light

Stationary objects have momentum of zero

Why No motion = no speed = no velocity = no momentum

Momentum is directly proportional to masshellip momentum increases as mass increases

P

Mass (kg)

Force

Force = the cause of acceleration or a change in velocity

- force is measured in units called Newtons

Net force = the combination of all the forces acting upon an object

bull The size of the arrow represents the amount of forcehellip

bull The arrows are the same so there is no movement

Friction

Friction = the force between two objects in contact that opposes the motion of either object

Pretend you are in a helicopter looking down on a ski slope in early springhellip The ice is meltinghellip Patches of dirt and gravel begin to showhellip

How much friction

Skis + snow = little frictionhellip skis move over snow

Skis + dirt = a lot of frictionhellip skis do not move over dirt

Air resistance is a type of friction

Gravity

Gravity = Force of attraction between 2 objects due to their masses

The force of gravity is different on different planets moons etc

On earth g = 98ms2

Gravity depends upon the masses as well as the distance between objects

Newtonrsquos Laws of Motion

Newtonrsquos 1st Law- the law of inertia

An object at rest remains at rest and an object in motion remains in motion unless it experiences an unbalanced force

bull Example 1 Whiplash ndash Person B is stopped at a traffic light Person A is not paying attention and rear-ends Person B

bull Result Person B moves forward suddenlyhellip Their head snaps back as it attempts to ldquoremain at restrdquo Their body attached to the seat moves forwardhellip their head snaps forward to catch up with the body resulting in whiplash

Example 2 Bus ride - The bus driver does not like children Every time they get too loud he slams on the breaks Why does he do this

Inertia = The tendency of an object to remain at rest or in motion with a constant velocity All objects have inertia because they resist changes in motion

Trivia If two people on a space ship (in space) get into a physical fight which will win

Person A Person B

Even though they are weightlesshellip there is no gravity Person A has a greater mass therefore a greater inertia

Newtonrsquos 2nd law of Motion- the law of acceleration

bull The unbalanced force acting on an object equals the objectrsquos mass times its acceleration

bull Force = Mass x Acceleration

Example pushing a cart

The greater the mass the more force needed to cause acceleration

Bumper cars

Car Speed

0

20

40

60

80

100

120

140

0 05 1 15 2 25

Time (hours)

Dis

t m

iles

Car A

Car B

Car C

bull What do you notice about the 3 lines on the Car Speed graph

ndashSteepness of line = greater the slope of the line

ndashthe greater the slope the faster the speed of the car

ndash slope = ∆ Y or rise

∆ X run

ndash If distance is placed on the y-axis and time is placed on the x-axis

Velocity = ∆ D = ∆ Y = Slope of line

∆ T ∆ X

bull So Velocity = Slope of line

Car A Slow Gradual line

Car B Medium Medium

Car C Fast Steep line

Graphing Velocity (Average Speed)

What can you tell from different graphs

bull 3 Different objects moving at 3 different speeds

T

D

bull Stopped Object Time passes but distance does not change

bull No movement T

D

bull Backward moving objecthellip

bull The distance is decreasing so there is movement towards the source

T

D

bull Circular Motion Time passes as the same distances are revisited like a race track

T

D

bull Series of motions

bull Rest-forward-rest-backward-rest

bull Note does not represent the profile of the terrain

T

D

Velocity Graphs and Profiles of Terrain

bull What do we know about movement

bull 1 ndash rest

bull 2 ndash gradual movement forward

bull 3 ndash rest

bull 4 ndash backward movement

bull 5 ndash rest

1

2

3

4

5

T

D

Velocity Graphs and Profiles of Terrain

bull 1 ndash You are halfway up a hill at rest holding a wagon

bull 2 ndash You start moving uphillbull 3 ndash You take a restbull 4 ndash The wagon handle slips

out of you hand and travels backward down the hill

bull 5 ndash The wagon stops moving at the bottom of the hill

1

2

3

4

5

T

D

bull What could be a possible explanation pulling a wagon uphill

Dimensional Analysis ndash Unit Analysis

In your head you can probably converthellip

hellip inches to feet

sure 12 in = 1 ft

hellip inches to yards

okay 3 ft in 1 yd = 36 in

hellip inches to miles

um probably not

bull FAQ When I convert from inches to yards or yards to inches when do I multiply and when do I divide

bull The easiest way to approach these unit conversions is by using dimensional analysis

There are 4 rules1 If you use only one unit to start put it over a

12 Determine the conversion factors (Ex 12

inches = 1 ft) and put into a fraction3 Properly place the conversion factors in an

equation4 Check cancellations of units so that you are

left with the unit you were looking for on the top of a division bar The units that are canceled should be on opposite sides of the division bar

Example 1 How many feet in 13 in 1 112 or 1083 ftStep 1hellip starting with 13 sohellip 13 inches

1

Step 2hellip conversion factors 1 foot or 12 inches 12 inches 1 foot

Step 3hellip place factors 13 inches x 1 foot 1 12 inches

Step 4hellip check cancellations 13 inches x 1 foot 1 12

inches

13 inches = 1083 ft

Example 2 Convert 13 inches into yards

Step 1hellip starting with 13 sohellip 13 in

1

Step 2hellip conversion factors 1 ft 1 yd

12 in 3 ft

Step 3hellip place factors 13 in x 1 ft x 1 yd =

1 12 in 3 ft

Step 4hellip check cancellations 13 in x 1 ft x 1 yd

1 12 in 3 ft

13 in = 036 yd

Example 3 Convert 2 years into seconds

2 yrs x 365 days x 24 h x 60 min x 60 sec

1 1 yr 1 day 1 h 1 min

2 yrs = 63072000 sec

Example 4 Convert 4 decades into minutes

4 dec x 10 yrs x 365 days x 24 h x 60 min

1 1 dec 1 yr 1 day 1 h

4 decades = 21024000 m

Example 5 I am 5rsquo 3rdquo or (5 x 12) + 3 = 63 inches tall How many cm tall am I

63 in x 256 cm =

1 1 in

63 in = 1601 cm

Dimensional Analysis Worksheet

1 In New Jersey students in public schools go to school for 4 years How many minutes are students enrolled in high school

4 years x 365 days x 24 h x 60 min

1 1 yr 1 day 1 h

4 yrs = 2102400 min

2 Alaynarsquos dog is 3 ft tall What is the dogrsquos height in mm

3 ft x 12 in x 254 cm x 10 mm

1 1 ft 1 in 1 cm

3 ft = 9144 mm

3 Brian and Jesse were on a bus trip going 50 MPH For some extra fun they decided to convert the busrsquos speed into kmh What should their answer be

50 miles x 161 km 1 hr 1 mile

50 MPH = 805 kmh

4 Driving home from practice Alexrsquos mother was driving at a speed of 30 ms What was their speed in kmh

30 m x 1 km x 60 s x 60 min 1 s 1000 m 1 min 1 h

30 ms = 108 kmh

5 Saskia was riding her bike down the road at a speed of 5 kmh What was her speed in ms

5 km x 1000 m x 1 hr x 1 min 1 h 1 km 60 min 60 s

5 kmh = 139 ms

Class experiment

1 Determine how tall you are in inches

2 Using the conversion factor 1 mile = 161 km determine how tall you are in cm

3 Check your answer with a meter stick

AccelerationWhen you accelerate what are you doing

Speeding uphellip accelerating

When you slow down what are you doing

Decelerating

In physics we use the same term ldquoaccelerationrdquo for both speeding up and slowing down We distinguish between the two by assigning positive or negative values

+ acceleration as in speeding up positive

- acceleration as in slowing down negative

Acceleration = the change in velocity over time

- measured in ms or ms2

s

Acceleration = ∆ Velocity

∆ Time

Acceleration = ∆ Distance + Direction

∆ Time

∆ Time

Given an object moving in a circle

- ∆ velocity due to a ∆ direction

- if ∆ velocity the ∆ acceleration as well

- circular motion = ∆ D = ∆ V = ∆ A

Graphing Acceleration

A = ∆ V and slope = ∆ Y

∆ T ∆ X

Acceleration = ∆ V = ∆ Y = Slope of line

∆ T ∆ X

So Acceleration = Slope of line

Steep slope = fast movement

Gradual slope = slow movement

Acceleration Deceleration

V

T

V

T

Steepness of the line indicates the degree of acceleration

V

T

V

T

Comparing Velocity and Acceleration

Velocity = ∆ Distance Acceleration = ∆ Velocity

∆ Time ∆ Time

D

T

These two lines indicate the exact same thing the same rate of acceleration

bull Acceleration = + slope

bull Deceleration = - slope

T

V

+ slope

- slope

When object is a rest Velocity is zero

If ∆ Distance = 0 then ∆ Velocityhellip so Acceleration = 0

D

T

V

T

0

When acceleration equals zero

A= ∆ V no change in velocity

∆ T Time will always pass

No change in velocity

- no velocity ndash V = 0 then object is at rest

- constant velocity - ∆ V = Vfinal ndash Vinitial

Vf = 50 milesh and Vi = 50 milesh

Then ∆ V = 0

If acceleration = zero you are either stopped or on cruise control

To determine which you must find if there is a change in distance

How it all fits togetherFrom Motion Acceleration only one variable is

added at a time1 Motion = ∆ Distance2 Speed = ∆ Distance

∆ Time3 Velocity = ∆ Distance + Direction

∆ Time4 Acceleration = ∆ Distance + Direction

∆ Time∆ Time

Momentum

When an object is in motion we think velocity However we must not forget Momentum ndash which is also acting on the object

Momentum = a quantity defined as the product of an objectrsquos mass and its velocity - In a formula P = momentum- momentum moves in the same direction as the velocity

P = Mass x Velocity

- Measured in kgms

Momentum and ∆ Velocity

- large momentum difficult to change velocity

- small momentum easier to change velocity

Class Experiment Red light green light

Stationary objects have momentum of zero

Why No motion = no speed = no velocity = no momentum

Momentum is directly proportional to masshellip momentum increases as mass increases

P

Mass (kg)

Force

Force = the cause of acceleration or a change in velocity

- force is measured in units called Newtons

Net force = the combination of all the forces acting upon an object

bull The size of the arrow represents the amount of forcehellip

bull The arrows are the same so there is no movement

Friction

Friction = the force between two objects in contact that opposes the motion of either object

Pretend you are in a helicopter looking down on a ski slope in early springhellip The ice is meltinghellip Patches of dirt and gravel begin to showhellip

How much friction

Skis + snow = little frictionhellip skis move over snow

Skis + dirt = a lot of frictionhellip skis do not move over dirt

Air resistance is a type of friction

Gravity

Gravity = Force of attraction between 2 objects due to their masses

The force of gravity is different on different planets moons etc

On earth g = 98ms2

Gravity depends upon the masses as well as the distance between objects

Newtonrsquos Laws of Motion

Newtonrsquos 1st Law- the law of inertia

An object at rest remains at rest and an object in motion remains in motion unless it experiences an unbalanced force

bull Example 1 Whiplash ndash Person B is stopped at a traffic light Person A is not paying attention and rear-ends Person B

bull Result Person B moves forward suddenlyhellip Their head snaps back as it attempts to ldquoremain at restrdquo Their body attached to the seat moves forwardhellip their head snaps forward to catch up with the body resulting in whiplash

Example 2 Bus ride - The bus driver does not like children Every time they get too loud he slams on the breaks Why does he do this

Inertia = The tendency of an object to remain at rest or in motion with a constant velocity All objects have inertia because they resist changes in motion

Trivia If two people on a space ship (in space) get into a physical fight which will win

Person A Person B

Even though they are weightlesshellip there is no gravity Person A has a greater mass therefore a greater inertia

Newtonrsquos 2nd law of Motion- the law of acceleration

bull The unbalanced force acting on an object equals the objectrsquos mass times its acceleration

bull Force = Mass x Acceleration

Example pushing a cart

The greater the mass the more force needed to cause acceleration

Bumper cars

bull What do you notice about the 3 lines on the Car Speed graph

ndashSteepness of line = greater the slope of the line

ndashthe greater the slope the faster the speed of the car

ndash slope = ∆ Y or rise

∆ X run

ndash If distance is placed on the y-axis and time is placed on the x-axis

Velocity = ∆ D = ∆ Y = Slope of line

∆ T ∆ X

bull So Velocity = Slope of line

Car A Slow Gradual line

Car B Medium Medium

Car C Fast Steep line

Graphing Velocity (Average Speed)

What can you tell from different graphs

bull 3 Different objects moving at 3 different speeds

T

D

bull Stopped Object Time passes but distance does not change

bull No movement T

D

bull Backward moving objecthellip

bull The distance is decreasing so there is movement towards the source

T

D

bull Circular Motion Time passes as the same distances are revisited like a race track

T

D

bull Series of motions

bull Rest-forward-rest-backward-rest

bull Note does not represent the profile of the terrain

T

D

Velocity Graphs and Profiles of Terrain

bull What do we know about movement

bull 1 ndash rest

bull 2 ndash gradual movement forward

bull 3 ndash rest

bull 4 ndash backward movement

bull 5 ndash rest

1

2

3

4

5

T

D

Velocity Graphs and Profiles of Terrain

bull 1 ndash You are halfway up a hill at rest holding a wagon

bull 2 ndash You start moving uphillbull 3 ndash You take a restbull 4 ndash The wagon handle slips

out of you hand and travels backward down the hill

bull 5 ndash The wagon stops moving at the bottom of the hill

1

2

3

4

5

T

D

bull What could be a possible explanation pulling a wagon uphill

Dimensional Analysis ndash Unit Analysis

In your head you can probably converthellip

hellip inches to feet

sure 12 in = 1 ft

hellip inches to yards

okay 3 ft in 1 yd = 36 in

hellip inches to miles

um probably not

bull FAQ When I convert from inches to yards or yards to inches when do I multiply and when do I divide

bull The easiest way to approach these unit conversions is by using dimensional analysis

There are 4 rules1 If you use only one unit to start put it over a

12 Determine the conversion factors (Ex 12

inches = 1 ft) and put into a fraction3 Properly place the conversion factors in an

equation4 Check cancellations of units so that you are

left with the unit you were looking for on the top of a division bar The units that are canceled should be on opposite sides of the division bar

Example 1 How many feet in 13 in 1 112 or 1083 ftStep 1hellip starting with 13 sohellip 13 inches

1

Step 2hellip conversion factors 1 foot or 12 inches 12 inches 1 foot

Step 3hellip place factors 13 inches x 1 foot 1 12 inches

Step 4hellip check cancellations 13 inches x 1 foot 1 12

inches

13 inches = 1083 ft

Example 2 Convert 13 inches into yards

Step 1hellip starting with 13 sohellip 13 in

1

Step 2hellip conversion factors 1 ft 1 yd

12 in 3 ft

Step 3hellip place factors 13 in x 1 ft x 1 yd =

1 12 in 3 ft

Step 4hellip check cancellations 13 in x 1 ft x 1 yd

1 12 in 3 ft

13 in = 036 yd

Example 3 Convert 2 years into seconds

2 yrs x 365 days x 24 h x 60 min x 60 sec

1 1 yr 1 day 1 h 1 min

2 yrs = 63072000 sec

Example 4 Convert 4 decades into minutes

4 dec x 10 yrs x 365 days x 24 h x 60 min

1 1 dec 1 yr 1 day 1 h

4 decades = 21024000 m

Example 5 I am 5rsquo 3rdquo or (5 x 12) + 3 = 63 inches tall How many cm tall am I

63 in x 256 cm =

1 1 in

63 in = 1601 cm

Dimensional Analysis Worksheet

1 In New Jersey students in public schools go to school for 4 years How many minutes are students enrolled in high school

4 years x 365 days x 24 h x 60 min

1 1 yr 1 day 1 h

4 yrs = 2102400 min

2 Alaynarsquos dog is 3 ft tall What is the dogrsquos height in mm

3 ft x 12 in x 254 cm x 10 mm

1 1 ft 1 in 1 cm

3 ft = 9144 mm

3 Brian and Jesse were on a bus trip going 50 MPH For some extra fun they decided to convert the busrsquos speed into kmh What should their answer be

50 miles x 161 km 1 hr 1 mile

50 MPH = 805 kmh

4 Driving home from practice Alexrsquos mother was driving at a speed of 30 ms What was their speed in kmh

30 m x 1 km x 60 s x 60 min 1 s 1000 m 1 min 1 h

30 ms = 108 kmh

5 Saskia was riding her bike down the road at a speed of 5 kmh What was her speed in ms

5 km x 1000 m x 1 hr x 1 min 1 h 1 km 60 min 60 s

5 kmh = 139 ms

Class experiment

1 Determine how tall you are in inches

2 Using the conversion factor 1 mile = 161 km determine how tall you are in cm

3 Check your answer with a meter stick

AccelerationWhen you accelerate what are you doing

Speeding uphellip accelerating

When you slow down what are you doing

Decelerating

In physics we use the same term ldquoaccelerationrdquo for both speeding up and slowing down We distinguish between the two by assigning positive or negative values

+ acceleration as in speeding up positive

- acceleration as in slowing down negative

Acceleration = the change in velocity over time

- measured in ms or ms2

s

Acceleration = ∆ Velocity

∆ Time

Acceleration = ∆ Distance + Direction

∆ Time

∆ Time

Given an object moving in a circle

- ∆ velocity due to a ∆ direction

- if ∆ velocity the ∆ acceleration as well

- circular motion = ∆ D = ∆ V = ∆ A

Graphing Acceleration

A = ∆ V and slope = ∆ Y

∆ T ∆ X

Acceleration = ∆ V = ∆ Y = Slope of line

∆ T ∆ X

So Acceleration = Slope of line

Steep slope = fast movement

Gradual slope = slow movement

Acceleration Deceleration

V

T

V

T

Steepness of the line indicates the degree of acceleration

V

T

V

T

Comparing Velocity and Acceleration

Velocity = ∆ Distance Acceleration = ∆ Velocity

∆ Time ∆ Time

D

T

These two lines indicate the exact same thing the same rate of acceleration

bull Acceleration = + slope

bull Deceleration = - slope

T

V

+ slope

- slope

When object is a rest Velocity is zero

If ∆ Distance = 0 then ∆ Velocityhellip so Acceleration = 0

D

T

V

T

0

When acceleration equals zero

A= ∆ V no change in velocity

∆ T Time will always pass

No change in velocity

- no velocity ndash V = 0 then object is at rest

- constant velocity - ∆ V = Vfinal ndash Vinitial

Vf = 50 milesh and Vi = 50 milesh

Then ∆ V = 0

If acceleration = zero you are either stopped or on cruise control

To determine which you must find if there is a change in distance

How it all fits togetherFrom Motion Acceleration only one variable is

added at a time1 Motion = ∆ Distance2 Speed = ∆ Distance

∆ Time3 Velocity = ∆ Distance + Direction

∆ Time4 Acceleration = ∆ Distance + Direction

∆ Time∆ Time

Momentum

When an object is in motion we think velocity However we must not forget Momentum ndash which is also acting on the object

Momentum = a quantity defined as the product of an objectrsquos mass and its velocity - In a formula P = momentum- momentum moves in the same direction as the velocity

P = Mass x Velocity

- Measured in kgms

Momentum and ∆ Velocity

- large momentum difficult to change velocity

- small momentum easier to change velocity

Class Experiment Red light green light

Stationary objects have momentum of zero

Why No motion = no speed = no velocity = no momentum

Momentum is directly proportional to masshellip momentum increases as mass increases

P

Mass (kg)

Force

Force = the cause of acceleration or a change in velocity

- force is measured in units called Newtons

Net force = the combination of all the forces acting upon an object

bull The size of the arrow represents the amount of forcehellip

bull The arrows are the same so there is no movement

Friction

Friction = the force between two objects in contact that opposes the motion of either object

Pretend you are in a helicopter looking down on a ski slope in early springhellip The ice is meltinghellip Patches of dirt and gravel begin to showhellip

How much friction

Skis + snow = little frictionhellip skis move over snow

Skis + dirt = a lot of frictionhellip skis do not move over dirt

Air resistance is a type of friction

Gravity

Gravity = Force of attraction between 2 objects due to their masses

The force of gravity is different on different planets moons etc

On earth g = 98ms2

Gravity depends upon the masses as well as the distance between objects

Newtonrsquos Laws of Motion

Newtonrsquos 1st Law- the law of inertia

An object at rest remains at rest and an object in motion remains in motion unless it experiences an unbalanced force

bull Example 1 Whiplash ndash Person B is stopped at a traffic light Person A is not paying attention and rear-ends Person B

bull Result Person B moves forward suddenlyhellip Their head snaps back as it attempts to ldquoremain at restrdquo Their body attached to the seat moves forwardhellip their head snaps forward to catch up with the body resulting in whiplash

Example 2 Bus ride - The bus driver does not like children Every time they get too loud he slams on the breaks Why does he do this

Inertia = The tendency of an object to remain at rest or in motion with a constant velocity All objects have inertia because they resist changes in motion

Trivia If two people on a space ship (in space) get into a physical fight which will win

Person A Person B

Even though they are weightlesshellip there is no gravity Person A has a greater mass therefore a greater inertia

Newtonrsquos 2nd law of Motion- the law of acceleration

bull The unbalanced force acting on an object equals the objectrsquos mass times its acceleration

bull Force = Mass x Acceleration

Example pushing a cart

The greater the mass the more force needed to cause acceleration

Bumper cars

ndash If distance is placed on the y-axis and time is placed on the x-axis

Velocity = ∆ D = ∆ Y = Slope of line

∆ T ∆ X

bull So Velocity = Slope of line

Car A Slow Gradual line

Car B Medium Medium

Car C Fast Steep line

Graphing Velocity (Average Speed)

What can you tell from different graphs

bull 3 Different objects moving at 3 different speeds

T

D

bull Stopped Object Time passes but distance does not change

bull No movement T

D

bull Backward moving objecthellip

bull The distance is decreasing so there is movement towards the source

T

D

bull Circular Motion Time passes as the same distances are revisited like a race track

T

D

bull Series of motions

bull Rest-forward-rest-backward-rest

bull Note does not represent the profile of the terrain

T

D

Velocity Graphs and Profiles of Terrain

bull What do we know about movement

bull 1 ndash rest

bull 2 ndash gradual movement forward

bull 3 ndash rest

bull 4 ndash backward movement

bull 5 ndash rest

1

2

3

4

5

T

D

Velocity Graphs and Profiles of Terrain

bull 1 ndash You are halfway up a hill at rest holding a wagon

bull 2 ndash You start moving uphillbull 3 ndash You take a restbull 4 ndash The wagon handle slips

out of you hand and travels backward down the hill

bull 5 ndash The wagon stops moving at the bottom of the hill

1

2

3

4

5

T

D

bull What could be a possible explanation pulling a wagon uphill

Dimensional Analysis ndash Unit Analysis

In your head you can probably converthellip

hellip inches to feet

sure 12 in = 1 ft

hellip inches to yards

okay 3 ft in 1 yd = 36 in

hellip inches to miles

um probably not

bull FAQ When I convert from inches to yards or yards to inches when do I multiply and when do I divide

bull The easiest way to approach these unit conversions is by using dimensional analysis

There are 4 rules1 If you use only one unit to start put it over a

12 Determine the conversion factors (Ex 12

inches = 1 ft) and put into a fraction3 Properly place the conversion factors in an

equation4 Check cancellations of units so that you are

left with the unit you were looking for on the top of a division bar The units that are canceled should be on opposite sides of the division bar

Example 1 How many feet in 13 in 1 112 or 1083 ftStep 1hellip starting with 13 sohellip 13 inches

1

Step 2hellip conversion factors 1 foot or 12 inches 12 inches 1 foot

Step 3hellip place factors 13 inches x 1 foot 1 12 inches

Step 4hellip check cancellations 13 inches x 1 foot 1 12

inches

13 inches = 1083 ft

Example 2 Convert 13 inches into yards

Step 1hellip starting with 13 sohellip 13 in

1

Step 2hellip conversion factors 1 ft 1 yd

12 in 3 ft

Step 3hellip place factors 13 in x 1 ft x 1 yd =

1 12 in 3 ft

Step 4hellip check cancellations 13 in x 1 ft x 1 yd

1 12 in 3 ft

13 in = 036 yd

Example 3 Convert 2 years into seconds

2 yrs x 365 days x 24 h x 60 min x 60 sec

1 1 yr 1 day 1 h 1 min

2 yrs = 63072000 sec

Example 4 Convert 4 decades into minutes

4 dec x 10 yrs x 365 days x 24 h x 60 min

1 1 dec 1 yr 1 day 1 h

4 decades = 21024000 m

Example 5 I am 5rsquo 3rdquo or (5 x 12) + 3 = 63 inches tall How many cm tall am I

63 in x 256 cm =

1 1 in

63 in = 1601 cm

Dimensional Analysis Worksheet

1 In New Jersey students in public schools go to school for 4 years How many minutes are students enrolled in high school

4 years x 365 days x 24 h x 60 min

1 1 yr 1 day 1 h

4 yrs = 2102400 min

2 Alaynarsquos dog is 3 ft tall What is the dogrsquos height in mm

3 ft x 12 in x 254 cm x 10 mm

1 1 ft 1 in 1 cm

3 ft = 9144 mm

3 Brian and Jesse were on a bus trip going 50 MPH For some extra fun they decided to convert the busrsquos speed into kmh What should their answer be

50 miles x 161 km 1 hr 1 mile

50 MPH = 805 kmh

4 Driving home from practice Alexrsquos mother was driving at a speed of 30 ms What was their speed in kmh

30 m x 1 km x 60 s x 60 min 1 s 1000 m 1 min 1 h

30 ms = 108 kmh

5 Saskia was riding her bike down the road at a speed of 5 kmh What was her speed in ms

5 km x 1000 m x 1 hr x 1 min 1 h 1 km 60 min 60 s

5 kmh = 139 ms

Class experiment

1 Determine how tall you are in inches

2 Using the conversion factor 1 mile = 161 km determine how tall you are in cm

3 Check your answer with a meter stick

AccelerationWhen you accelerate what are you doing

Speeding uphellip accelerating

When you slow down what are you doing

Decelerating

In physics we use the same term ldquoaccelerationrdquo for both speeding up and slowing down We distinguish between the two by assigning positive or negative values

+ acceleration as in speeding up positive

- acceleration as in slowing down negative

Acceleration = the change in velocity over time

- measured in ms or ms2

s

Acceleration = ∆ Velocity

∆ Time

Acceleration = ∆ Distance + Direction

∆ Time

∆ Time

Given an object moving in a circle

- ∆ velocity due to a ∆ direction

- if ∆ velocity the ∆ acceleration as well

- circular motion = ∆ D = ∆ V = ∆ A

Graphing Acceleration

A = ∆ V and slope = ∆ Y

∆ T ∆ X

Acceleration = ∆ V = ∆ Y = Slope of line

∆ T ∆ X

So Acceleration = Slope of line

Steep slope = fast movement

Gradual slope = slow movement

Acceleration Deceleration

V

T

V

T

Steepness of the line indicates the degree of acceleration

V

T

V

T

Comparing Velocity and Acceleration

Velocity = ∆ Distance Acceleration = ∆ Velocity

∆ Time ∆ Time

D

T

These two lines indicate the exact same thing the same rate of acceleration

bull Acceleration = + slope

bull Deceleration = - slope

T

V

+ slope

- slope

When object is a rest Velocity is zero

If ∆ Distance = 0 then ∆ Velocityhellip so Acceleration = 0

D

T

V

T

0

When acceleration equals zero

A= ∆ V no change in velocity

∆ T Time will always pass

No change in velocity

- no velocity ndash V = 0 then object is at rest

- constant velocity - ∆ V = Vfinal ndash Vinitial

Vf = 50 milesh and Vi = 50 milesh

Then ∆ V = 0

If acceleration = zero you are either stopped or on cruise control

To determine which you must find if there is a change in distance

How it all fits togetherFrom Motion Acceleration only one variable is

added at a time1 Motion = ∆ Distance2 Speed = ∆ Distance

∆ Time3 Velocity = ∆ Distance + Direction

∆ Time4 Acceleration = ∆ Distance + Direction

∆ Time∆ Time

Momentum

When an object is in motion we think velocity However we must not forget Momentum ndash which is also acting on the object

Momentum = a quantity defined as the product of an objectrsquos mass and its velocity - In a formula P = momentum- momentum moves in the same direction as the velocity

P = Mass x Velocity

- Measured in kgms

Momentum and ∆ Velocity

- large momentum difficult to change velocity

- small momentum easier to change velocity

Class Experiment Red light green light

Stationary objects have momentum of zero

Why No motion = no speed = no velocity = no momentum

Momentum is directly proportional to masshellip momentum increases as mass increases

P

Mass (kg)

Force

Force = the cause of acceleration or a change in velocity

- force is measured in units called Newtons

Net force = the combination of all the forces acting upon an object

bull The size of the arrow represents the amount of forcehellip

bull The arrows are the same so there is no movement

Friction

Friction = the force between two objects in contact that opposes the motion of either object

Pretend you are in a helicopter looking down on a ski slope in early springhellip The ice is meltinghellip Patches of dirt and gravel begin to showhellip

How much friction

Skis + snow = little frictionhellip skis move over snow

Skis + dirt = a lot of frictionhellip skis do not move over dirt

Air resistance is a type of friction

Gravity

Gravity = Force of attraction between 2 objects due to their masses

The force of gravity is different on different planets moons etc

On earth g = 98ms2

Gravity depends upon the masses as well as the distance between objects

Newtonrsquos Laws of Motion

Newtonrsquos 1st Law- the law of inertia

An object at rest remains at rest and an object in motion remains in motion unless it experiences an unbalanced force

bull Example 1 Whiplash ndash Person B is stopped at a traffic light Person A is not paying attention and rear-ends Person B

bull Result Person B moves forward suddenlyhellip Their head snaps back as it attempts to ldquoremain at restrdquo Their body attached to the seat moves forwardhellip their head snaps forward to catch up with the body resulting in whiplash

Example 2 Bus ride - The bus driver does not like children Every time they get too loud he slams on the breaks Why does he do this

Inertia = The tendency of an object to remain at rest or in motion with a constant velocity All objects have inertia because they resist changes in motion

Trivia If two people on a space ship (in space) get into a physical fight which will win

Person A Person B

Even though they are weightlesshellip there is no gravity Person A has a greater mass therefore a greater inertia

Newtonrsquos 2nd law of Motion- the law of acceleration

bull The unbalanced force acting on an object equals the objectrsquos mass times its acceleration

bull Force = Mass x Acceleration

Example pushing a cart

The greater the mass the more force needed to cause acceleration

Bumper cars

Graphing Velocity (Average Speed)

What can you tell from different graphs

bull 3 Different objects moving at 3 different speeds

T

D

bull Stopped Object Time passes but distance does not change

bull No movement T

D

bull Backward moving objecthellip

bull The distance is decreasing so there is movement towards the source

T

D

bull Circular Motion Time passes as the same distances are revisited like a race track

T

D

bull Series of motions

bull Rest-forward-rest-backward-rest

bull Note does not represent the profile of the terrain

T

D

Velocity Graphs and Profiles of Terrain

bull What do we know about movement

bull 1 ndash rest

bull 2 ndash gradual movement forward

bull 3 ndash rest

bull 4 ndash backward movement

bull 5 ndash rest

1

2

3

4

5

T

D

Velocity Graphs and Profiles of Terrain

bull 1 ndash You are halfway up a hill at rest holding a wagon

bull 2 ndash You start moving uphillbull 3 ndash You take a restbull 4 ndash The wagon handle slips

out of you hand and travels backward down the hill

bull 5 ndash The wagon stops moving at the bottom of the hill

1

2

3

4

5

T

D

bull What could be a possible explanation pulling a wagon uphill

Dimensional Analysis ndash Unit Analysis

In your head you can probably converthellip

hellip inches to feet

sure 12 in = 1 ft

hellip inches to yards

okay 3 ft in 1 yd = 36 in

hellip inches to miles

um probably not

bull FAQ When I convert from inches to yards or yards to inches when do I multiply and when do I divide

bull The easiest way to approach these unit conversions is by using dimensional analysis

There are 4 rules1 If you use only one unit to start put it over a

12 Determine the conversion factors (Ex 12

inches = 1 ft) and put into a fraction3 Properly place the conversion factors in an

equation4 Check cancellations of units so that you are

left with the unit you were looking for on the top of a division bar The units that are canceled should be on opposite sides of the division bar

Example 1 How many feet in 13 in 1 112 or 1083 ftStep 1hellip starting with 13 sohellip 13 inches

1

Step 2hellip conversion factors 1 foot or 12 inches 12 inches 1 foot

Step 3hellip place factors 13 inches x 1 foot 1 12 inches

Step 4hellip check cancellations 13 inches x 1 foot 1 12

inches

13 inches = 1083 ft

Example 2 Convert 13 inches into yards

Step 1hellip starting with 13 sohellip 13 in

1

Step 2hellip conversion factors 1 ft 1 yd

12 in 3 ft

Step 3hellip place factors 13 in x 1 ft x 1 yd =

1 12 in 3 ft

Step 4hellip check cancellations 13 in x 1 ft x 1 yd

1 12 in 3 ft

13 in = 036 yd

Example 3 Convert 2 years into seconds

2 yrs x 365 days x 24 h x 60 min x 60 sec

1 1 yr 1 day 1 h 1 min

2 yrs = 63072000 sec

Example 4 Convert 4 decades into minutes

4 dec x 10 yrs x 365 days x 24 h x 60 min

1 1 dec 1 yr 1 day 1 h

4 decades = 21024000 m

Example 5 I am 5rsquo 3rdquo or (5 x 12) + 3 = 63 inches tall How many cm tall am I

63 in x 256 cm =

1 1 in

63 in = 1601 cm

Dimensional Analysis Worksheet

1 In New Jersey students in public schools go to school for 4 years How many minutes are students enrolled in high school

4 years x 365 days x 24 h x 60 min

1 1 yr 1 day 1 h

4 yrs = 2102400 min

2 Alaynarsquos dog is 3 ft tall What is the dogrsquos height in mm

3 ft x 12 in x 254 cm x 10 mm

1 1 ft 1 in 1 cm

3 ft = 9144 mm

3 Brian and Jesse were on a bus trip going 50 MPH For some extra fun they decided to convert the busrsquos speed into kmh What should their answer be

50 miles x 161 km 1 hr 1 mile

50 MPH = 805 kmh

4 Driving home from practice Alexrsquos mother was driving at a speed of 30 ms What was their speed in kmh

30 m x 1 km x 60 s x 60 min 1 s 1000 m 1 min 1 h

30 ms = 108 kmh

5 Saskia was riding her bike down the road at a speed of 5 kmh What was her speed in ms

5 km x 1000 m x 1 hr x 1 min 1 h 1 km 60 min 60 s

5 kmh = 139 ms

Class experiment

1 Determine how tall you are in inches

2 Using the conversion factor 1 mile = 161 km determine how tall you are in cm

3 Check your answer with a meter stick

AccelerationWhen you accelerate what are you doing

Speeding uphellip accelerating

When you slow down what are you doing

Decelerating

In physics we use the same term ldquoaccelerationrdquo for both speeding up and slowing down We distinguish between the two by assigning positive or negative values

+ acceleration as in speeding up positive

- acceleration as in slowing down negative

Acceleration = the change in velocity over time

- measured in ms or ms2

s

Acceleration = ∆ Velocity

∆ Time

Acceleration = ∆ Distance + Direction

∆ Time

∆ Time

Given an object moving in a circle

- ∆ velocity due to a ∆ direction

- if ∆ velocity the ∆ acceleration as well

- circular motion = ∆ D = ∆ V = ∆ A

Graphing Acceleration

A = ∆ V and slope = ∆ Y

∆ T ∆ X

Acceleration = ∆ V = ∆ Y = Slope of line

∆ T ∆ X

So Acceleration = Slope of line

Steep slope = fast movement

Gradual slope = slow movement

Acceleration Deceleration

V

T

V

T

Steepness of the line indicates the degree of acceleration

V

T

V

T

Comparing Velocity and Acceleration

Velocity = ∆ Distance Acceleration = ∆ Velocity

∆ Time ∆ Time

D

T

These two lines indicate the exact same thing the same rate of acceleration

bull Acceleration = + slope

bull Deceleration = - slope

T

V

+ slope

- slope

When object is a rest Velocity is zero

If ∆ Distance = 0 then ∆ Velocityhellip so Acceleration = 0

D

T

V

T

0

When acceleration equals zero

A= ∆ V no change in velocity

∆ T Time will always pass

No change in velocity

- no velocity ndash V = 0 then object is at rest

- constant velocity - ∆ V = Vfinal ndash Vinitial

Vf = 50 milesh and Vi = 50 milesh

Then ∆ V = 0

If acceleration = zero you are either stopped or on cruise control

To determine which you must find if there is a change in distance

How it all fits togetherFrom Motion Acceleration only one variable is

added at a time1 Motion = ∆ Distance2 Speed = ∆ Distance

∆ Time3 Velocity = ∆ Distance + Direction

∆ Time4 Acceleration = ∆ Distance + Direction

∆ Time∆ Time

Momentum

When an object is in motion we think velocity However we must not forget Momentum ndash which is also acting on the object

Momentum = a quantity defined as the product of an objectrsquos mass and its velocity - In a formula P = momentum- momentum moves in the same direction as the velocity

P = Mass x Velocity

- Measured in kgms

Momentum and ∆ Velocity

- large momentum difficult to change velocity

- small momentum easier to change velocity

Class Experiment Red light green light

Stationary objects have momentum of zero

Why No motion = no speed = no velocity = no momentum

Momentum is directly proportional to masshellip momentum increases as mass increases

P

Mass (kg)

Force

Force = the cause of acceleration or a change in velocity

- force is measured in units called Newtons

Net force = the combination of all the forces acting upon an object

bull The size of the arrow represents the amount of forcehellip

bull The arrows are the same so there is no movement

Friction

Friction = the force between two objects in contact that opposes the motion of either object

Pretend you are in a helicopter looking down on a ski slope in early springhellip The ice is meltinghellip Patches of dirt and gravel begin to showhellip

How much friction

Skis + snow = little frictionhellip skis move over snow

Skis + dirt = a lot of frictionhellip skis do not move over dirt

Air resistance is a type of friction

Gravity

Gravity = Force of attraction between 2 objects due to their masses

The force of gravity is different on different planets moons etc

On earth g = 98ms2

Gravity depends upon the masses as well as the distance between objects

Newtonrsquos Laws of Motion

Newtonrsquos 1st Law- the law of inertia

An object at rest remains at rest and an object in motion remains in motion unless it experiences an unbalanced force

bull Example 1 Whiplash ndash Person B is stopped at a traffic light Person A is not paying attention and rear-ends Person B

bull Result Person B moves forward suddenlyhellip Their head snaps back as it attempts to ldquoremain at restrdquo Their body attached to the seat moves forwardhellip their head snaps forward to catch up with the body resulting in whiplash

Example 2 Bus ride - The bus driver does not like children Every time they get too loud he slams on the breaks Why does he do this

Inertia = The tendency of an object to remain at rest or in motion with a constant velocity All objects have inertia because they resist changes in motion

Trivia If two people on a space ship (in space) get into a physical fight which will win

Person A Person B

Even though they are weightlesshellip there is no gravity Person A has a greater mass therefore a greater inertia

Newtonrsquos 2nd law of Motion- the law of acceleration

bull The unbalanced force acting on an object equals the objectrsquos mass times its acceleration

bull Force = Mass x Acceleration

Example pushing a cart

The greater the mass the more force needed to cause acceleration

Bumper cars

bull Stopped Object Time passes but distance does not change

bull No movement T

D

bull Backward moving objecthellip

bull The distance is decreasing so there is movement towards the source

T

D

bull Circular Motion Time passes as the same distances are revisited like a race track

T

D

bull Series of motions

bull Rest-forward-rest-backward-rest

bull Note does not represent the profile of the terrain

T

D

Velocity Graphs and Profiles of Terrain

bull What do we know about movement

bull 1 ndash rest

bull 2 ndash gradual movement forward

bull 3 ndash rest

bull 4 ndash backward movement

bull 5 ndash rest

1

2

3

4

5

T

D

Velocity Graphs and Profiles of Terrain

bull 1 ndash You are halfway up a hill at rest holding a wagon

bull 2 ndash You start moving uphillbull 3 ndash You take a restbull 4 ndash The wagon handle slips

out of you hand and travels backward down the hill

bull 5 ndash The wagon stops moving at the bottom of the hill

1

2

3

4

5

T

D

bull What could be a possible explanation pulling a wagon uphill

Dimensional Analysis ndash Unit Analysis

In your head you can probably converthellip

hellip inches to feet

sure 12 in = 1 ft

hellip inches to yards

okay 3 ft in 1 yd = 36 in

hellip inches to miles

um probably not

bull FAQ When I convert from inches to yards or yards to inches when do I multiply and when do I divide

bull The easiest way to approach these unit conversions is by using dimensional analysis

There are 4 rules1 If you use only one unit to start put it over a

12 Determine the conversion factors (Ex 12

inches = 1 ft) and put into a fraction3 Properly place the conversion factors in an

equation4 Check cancellations of units so that you are

left with the unit you were looking for on the top of a division bar The units that are canceled should be on opposite sides of the division bar

Example 1 How many feet in 13 in 1 112 or 1083 ftStep 1hellip starting with 13 sohellip 13 inches

1

Step 2hellip conversion factors 1 foot or 12 inches 12 inches 1 foot

Step 3hellip place factors 13 inches x 1 foot 1 12 inches

Step 4hellip check cancellations 13 inches x 1 foot 1 12

inches

13 inches = 1083 ft

Example 2 Convert 13 inches into yards

Step 1hellip starting with 13 sohellip 13 in

1

Step 2hellip conversion factors 1 ft 1 yd

12 in 3 ft

Step 3hellip place factors 13 in x 1 ft x 1 yd =

1 12 in 3 ft

Step 4hellip check cancellations 13 in x 1 ft x 1 yd

1 12 in 3 ft

13 in = 036 yd

Example 3 Convert 2 years into seconds

2 yrs x 365 days x 24 h x 60 min x 60 sec

1 1 yr 1 day 1 h 1 min

2 yrs = 63072000 sec

Example 4 Convert 4 decades into minutes

4 dec x 10 yrs x 365 days x 24 h x 60 min

1 1 dec 1 yr 1 day 1 h

4 decades = 21024000 m

Example 5 I am 5rsquo 3rdquo or (5 x 12) + 3 = 63 inches tall How many cm tall am I

63 in x 256 cm =

1 1 in

63 in = 1601 cm

Dimensional Analysis Worksheet

1 In New Jersey students in public schools go to school for 4 years How many minutes are students enrolled in high school

4 years x 365 days x 24 h x 60 min

1 1 yr 1 day 1 h

4 yrs = 2102400 min

2 Alaynarsquos dog is 3 ft tall What is the dogrsquos height in mm

3 ft x 12 in x 254 cm x 10 mm

1 1 ft 1 in 1 cm

3 ft = 9144 mm

3 Brian and Jesse were on a bus trip going 50 MPH For some extra fun they decided to convert the busrsquos speed into kmh What should their answer be

50 miles x 161 km 1 hr 1 mile

50 MPH = 805 kmh

4 Driving home from practice Alexrsquos mother was driving at a speed of 30 ms What was their speed in kmh

30 m x 1 km x 60 s x 60 min 1 s 1000 m 1 min 1 h

30 ms = 108 kmh

5 Saskia was riding her bike down the road at a speed of 5 kmh What was her speed in ms

5 km x 1000 m x 1 hr x 1 min 1 h 1 km 60 min 60 s

5 kmh = 139 ms

Class experiment

1 Determine how tall you are in inches

2 Using the conversion factor 1 mile = 161 km determine how tall you are in cm

3 Check your answer with a meter stick

AccelerationWhen you accelerate what are you doing

Speeding uphellip accelerating

When you slow down what are you doing

Decelerating

In physics we use the same term ldquoaccelerationrdquo for both speeding up and slowing down We distinguish between the two by assigning positive or negative values

+ acceleration as in speeding up positive

- acceleration as in slowing down negative

Acceleration = the change in velocity over time

- measured in ms or ms2

s

Acceleration = ∆ Velocity

∆ Time

Acceleration = ∆ Distance + Direction

∆ Time

∆ Time

Given an object moving in a circle

- ∆ velocity due to a ∆ direction

- if ∆ velocity the ∆ acceleration as well

- circular motion = ∆ D = ∆ V = ∆ A

Graphing Acceleration

A = ∆ V and slope = ∆ Y

∆ T ∆ X

Acceleration = ∆ V = ∆ Y = Slope of line

∆ T ∆ X

So Acceleration = Slope of line

Steep slope = fast movement

Gradual slope = slow movement

Acceleration Deceleration

V

T

V

T

Steepness of the line indicates the degree of acceleration

V

T

V

T

Comparing Velocity and Acceleration

Velocity = ∆ Distance Acceleration = ∆ Velocity

∆ Time ∆ Time

D

T

These two lines indicate the exact same thing the same rate of acceleration

bull Acceleration = + slope

bull Deceleration = - slope

T

V

+ slope

- slope

When object is a rest Velocity is zero

If ∆ Distance = 0 then ∆ Velocityhellip so Acceleration = 0

D

T

V

T

0

When acceleration equals zero

A= ∆ V no change in velocity

∆ T Time will always pass

No change in velocity

- no velocity ndash V = 0 then object is at rest

- constant velocity - ∆ V = Vfinal ndash Vinitial

Vf = 50 milesh and Vi = 50 milesh

Then ∆ V = 0

If acceleration = zero you are either stopped or on cruise control

To determine which you must find if there is a change in distance

How it all fits togetherFrom Motion Acceleration only one variable is

added at a time1 Motion = ∆ Distance2 Speed = ∆ Distance

∆ Time3 Velocity = ∆ Distance + Direction

∆ Time4 Acceleration = ∆ Distance + Direction

∆ Time∆ Time

Momentum

When an object is in motion we think velocity However we must not forget Momentum ndash which is also acting on the object

Momentum = a quantity defined as the product of an objectrsquos mass and its velocity - In a formula P = momentum- momentum moves in the same direction as the velocity

P = Mass x Velocity

- Measured in kgms

Momentum and ∆ Velocity

- large momentum difficult to change velocity

- small momentum easier to change velocity

Class Experiment Red light green light

Stationary objects have momentum of zero

Why No motion = no speed = no velocity = no momentum

Momentum is directly proportional to masshellip momentum increases as mass increases

P

Mass (kg)

Force

Force = the cause of acceleration or a change in velocity

- force is measured in units called Newtons

Net force = the combination of all the forces acting upon an object

bull The size of the arrow represents the amount of forcehellip

bull The arrows are the same so there is no movement

Friction

Friction = the force between two objects in contact that opposes the motion of either object

Pretend you are in a helicopter looking down on a ski slope in early springhellip The ice is meltinghellip Patches of dirt and gravel begin to showhellip

How much friction

Skis + snow = little frictionhellip skis move over snow

Skis + dirt = a lot of frictionhellip skis do not move over dirt

Air resistance is a type of friction

Gravity

Gravity = Force of attraction between 2 objects due to their masses

The force of gravity is different on different planets moons etc

On earth g = 98ms2

Gravity depends upon the masses as well as the distance between objects

Newtonrsquos Laws of Motion

Newtonrsquos 1st Law- the law of inertia

An object at rest remains at rest and an object in motion remains in motion unless it experiences an unbalanced force

bull Example 1 Whiplash ndash Person B is stopped at a traffic light Person A is not paying attention and rear-ends Person B

bull Result Person B moves forward suddenlyhellip Their head snaps back as it attempts to ldquoremain at restrdquo Their body attached to the seat moves forwardhellip their head snaps forward to catch up with the body resulting in whiplash

Example 2 Bus ride - The bus driver does not like children Every time they get too loud he slams on the breaks Why does he do this

Inertia = The tendency of an object to remain at rest or in motion with a constant velocity All objects have inertia because they resist changes in motion

Trivia If two people on a space ship (in space) get into a physical fight which will win

Person A Person B

Even though they are weightlesshellip there is no gravity Person A has a greater mass therefore a greater inertia

Newtonrsquos 2nd law of Motion- the law of acceleration

bull The unbalanced force acting on an object equals the objectrsquos mass times its acceleration

bull Force = Mass x Acceleration

Example pushing a cart

The greater the mass the more force needed to cause acceleration

Bumper cars

bull Backward moving objecthellip

bull The distance is decreasing so there is movement towards the source

T

D

bull Circular Motion Time passes as the same distances are revisited like a race track

T

D

bull Series of motions

bull Rest-forward-rest-backward-rest

bull Note does not represent the profile of the terrain

T

D

Velocity Graphs and Profiles of Terrain

bull What do we know about movement

bull 1 ndash rest

bull 2 ndash gradual movement forward

bull 3 ndash rest

bull 4 ndash backward movement

bull 5 ndash rest

1

2

3

4

5

T

D

Velocity Graphs and Profiles of Terrain

bull 1 ndash You are halfway up a hill at rest holding a wagon

bull 2 ndash You start moving uphillbull 3 ndash You take a restbull 4 ndash The wagon handle slips

out of you hand and travels backward down the hill

bull 5 ndash The wagon stops moving at the bottom of the hill

1

2

3

4

5

T

D

bull What could be a possible explanation pulling a wagon uphill

Dimensional Analysis ndash Unit Analysis

In your head you can probably converthellip

hellip inches to feet

sure 12 in = 1 ft

hellip inches to yards

okay 3 ft in 1 yd = 36 in

hellip inches to miles

um probably not

bull FAQ When I convert from inches to yards or yards to inches when do I multiply and when do I divide

bull The easiest way to approach these unit conversions is by using dimensional analysis

There are 4 rules1 If you use only one unit to start put it over a

12 Determine the conversion factors (Ex 12

inches = 1 ft) and put into a fraction3 Properly place the conversion factors in an

equation4 Check cancellations of units so that you are

left with the unit you were looking for on the top of a division bar The units that are canceled should be on opposite sides of the division bar

Example 1 How many feet in 13 in 1 112 or 1083 ftStep 1hellip starting with 13 sohellip 13 inches

1

Step 2hellip conversion factors 1 foot or 12 inches 12 inches 1 foot

Step 3hellip place factors 13 inches x 1 foot 1 12 inches

Step 4hellip check cancellations 13 inches x 1 foot 1 12

inches

13 inches = 1083 ft

Example 2 Convert 13 inches into yards

Step 1hellip starting with 13 sohellip 13 in

1

Step 2hellip conversion factors 1 ft 1 yd

12 in 3 ft

Step 3hellip place factors 13 in x 1 ft x 1 yd =

1 12 in 3 ft

Step 4hellip check cancellations 13 in x 1 ft x 1 yd

1 12 in 3 ft

13 in = 036 yd

Example 3 Convert 2 years into seconds

2 yrs x 365 days x 24 h x 60 min x 60 sec

1 1 yr 1 day 1 h 1 min

2 yrs = 63072000 sec

Example 4 Convert 4 decades into minutes

4 dec x 10 yrs x 365 days x 24 h x 60 min

1 1 dec 1 yr 1 day 1 h

4 decades = 21024000 m

Example 5 I am 5rsquo 3rdquo or (5 x 12) + 3 = 63 inches tall How many cm tall am I

63 in x 256 cm =

1 1 in

63 in = 1601 cm

Dimensional Analysis Worksheet

1 In New Jersey students in public schools go to school for 4 years How many minutes are students enrolled in high school

4 years x 365 days x 24 h x 60 min

1 1 yr 1 day 1 h

4 yrs = 2102400 min

2 Alaynarsquos dog is 3 ft tall What is the dogrsquos height in mm

3 ft x 12 in x 254 cm x 10 mm

1 1 ft 1 in 1 cm

3 ft = 9144 mm

3 Brian and Jesse were on a bus trip going 50 MPH For some extra fun they decided to convert the busrsquos speed into kmh What should their answer be

50 miles x 161 km 1 hr 1 mile

50 MPH = 805 kmh

4 Driving home from practice Alexrsquos mother was driving at a speed of 30 ms What was their speed in kmh

30 m x 1 km x 60 s x 60 min 1 s 1000 m 1 min 1 h

30 ms = 108 kmh

5 Saskia was riding her bike down the road at a speed of 5 kmh What was her speed in ms

5 km x 1000 m x 1 hr x 1 min 1 h 1 km 60 min 60 s

5 kmh = 139 ms

Class experiment

1 Determine how tall you are in inches

2 Using the conversion factor 1 mile = 161 km determine how tall you are in cm

3 Check your answer with a meter stick

AccelerationWhen you accelerate what are you doing

Speeding uphellip accelerating

When you slow down what are you doing

Decelerating

In physics we use the same term ldquoaccelerationrdquo for both speeding up and slowing down We distinguish between the two by assigning positive or negative values

+ acceleration as in speeding up positive

- acceleration as in slowing down negative

Acceleration = the change in velocity over time

- measured in ms or ms2

s

Acceleration = ∆ Velocity

∆ Time

Acceleration = ∆ Distance + Direction

∆ Time

∆ Time

Given an object moving in a circle

- ∆ velocity due to a ∆ direction

- if ∆ velocity the ∆ acceleration as well

- circular motion = ∆ D = ∆ V = ∆ A

Graphing Acceleration

A = ∆ V and slope = ∆ Y

∆ T ∆ X

Acceleration = ∆ V = ∆ Y = Slope of line

∆ T ∆ X

So Acceleration = Slope of line

Steep slope = fast movement

Gradual slope = slow movement

Acceleration Deceleration

V

T

V

T

Steepness of the line indicates the degree of acceleration

V

T

V

T

Comparing Velocity and Acceleration

Velocity = ∆ Distance Acceleration = ∆ Velocity

∆ Time ∆ Time

D

T

These two lines indicate the exact same thing the same rate of acceleration

bull Acceleration = + slope

bull Deceleration = - slope

T

V

+ slope

- slope

When object is a rest Velocity is zero

If ∆ Distance = 0 then ∆ Velocityhellip so Acceleration = 0

D

T

V

T

0

When acceleration equals zero

A= ∆ V no change in velocity

∆ T Time will always pass

No change in velocity

- no velocity ndash V = 0 then object is at rest

- constant velocity - ∆ V = Vfinal ndash Vinitial

Vf = 50 milesh and Vi = 50 milesh

Then ∆ V = 0

If acceleration = zero you are either stopped or on cruise control

To determine which you must find if there is a change in distance

How it all fits togetherFrom Motion Acceleration only one variable is

added at a time1 Motion = ∆ Distance2 Speed = ∆ Distance

∆ Time3 Velocity = ∆ Distance + Direction

∆ Time4 Acceleration = ∆ Distance + Direction

∆ Time∆ Time

Momentum

When an object is in motion we think velocity However we must not forget Momentum ndash which is also acting on the object

Momentum = a quantity defined as the product of an objectrsquos mass and its velocity - In a formula P = momentum- momentum moves in the same direction as the velocity

P = Mass x Velocity

- Measured in kgms

Momentum and ∆ Velocity

- large momentum difficult to change velocity

- small momentum easier to change velocity

Class Experiment Red light green light

Stationary objects have momentum of zero

Why No motion = no speed = no velocity = no momentum

Momentum is directly proportional to masshellip momentum increases as mass increases

P

Mass (kg)

Force

Force = the cause of acceleration or a change in velocity

- force is measured in units called Newtons

Net force = the combination of all the forces acting upon an object

bull The size of the arrow represents the amount of forcehellip

bull The arrows are the same so there is no movement

Friction

Friction = the force between two objects in contact that opposes the motion of either object

Pretend you are in a helicopter looking down on a ski slope in early springhellip The ice is meltinghellip Patches of dirt and gravel begin to showhellip

How much friction

Skis + snow = little frictionhellip skis move over snow

Skis + dirt = a lot of frictionhellip skis do not move over dirt

Air resistance is a type of friction

Gravity

Gravity = Force of attraction between 2 objects due to their masses

The force of gravity is different on different planets moons etc

On earth g = 98ms2

Gravity depends upon the masses as well as the distance between objects

Newtonrsquos Laws of Motion

Newtonrsquos 1st Law- the law of inertia

An object at rest remains at rest and an object in motion remains in motion unless it experiences an unbalanced force

bull Example 1 Whiplash ndash Person B is stopped at a traffic light Person A is not paying attention and rear-ends Person B

bull Result Person B moves forward suddenlyhellip Their head snaps back as it attempts to ldquoremain at restrdquo Their body attached to the seat moves forwardhellip their head snaps forward to catch up with the body resulting in whiplash

Example 2 Bus ride - The bus driver does not like children Every time they get too loud he slams on the breaks Why does he do this

Inertia = The tendency of an object to remain at rest or in motion with a constant velocity All objects have inertia because they resist changes in motion

Trivia If two people on a space ship (in space) get into a physical fight which will win

Person A Person B

Even though they are weightlesshellip there is no gravity Person A has a greater mass therefore a greater inertia

Newtonrsquos 2nd law of Motion- the law of acceleration

bull The unbalanced force acting on an object equals the objectrsquos mass times its acceleration

bull Force = Mass x Acceleration

Example pushing a cart

The greater the mass the more force needed to cause acceleration

Bumper cars

bull Circular Motion Time passes as the same distances are revisited like a race track

T

D

bull Series of motions

bull Rest-forward-rest-backward-rest

bull Note does not represent the profile of the terrain

T

D

Velocity Graphs and Profiles of Terrain

bull What do we know about movement

bull 1 ndash rest

bull 2 ndash gradual movement forward

bull 3 ndash rest

bull 4 ndash backward movement

bull 5 ndash rest

1

2

3

4

5

T

D

Velocity Graphs and Profiles of Terrain

bull 1 ndash You are halfway up a hill at rest holding a wagon

bull 2 ndash You start moving uphillbull 3 ndash You take a restbull 4 ndash The wagon handle slips

out of you hand and travels backward down the hill

bull 5 ndash The wagon stops moving at the bottom of the hill

1

2

3

4

5

T

D

bull What could be a possible explanation pulling a wagon uphill

Dimensional Analysis ndash Unit Analysis

In your head you can probably converthellip

hellip inches to feet

sure 12 in = 1 ft

hellip inches to yards

okay 3 ft in 1 yd = 36 in

hellip inches to miles

um probably not

bull FAQ When I convert from inches to yards or yards to inches when do I multiply and when do I divide

bull The easiest way to approach these unit conversions is by using dimensional analysis

There are 4 rules1 If you use only one unit to start put it over a

12 Determine the conversion factors (Ex 12

inches = 1 ft) and put into a fraction3 Properly place the conversion factors in an

equation4 Check cancellations of units so that you are

left with the unit you were looking for on the top of a division bar The units that are canceled should be on opposite sides of the division bar

Example 1 How many feet in 13 in 1 112 or 1083 ftStep 1hellip starting with 13 sohellip 13 inches

1

Step 2hellip conversion factors 1 foot or 12 inches 12 inches 1 foot

Step 3hellip place factors 13 inches x 1 foot 1 12 inches

Step 4hellip check cancellations 13 inches x 1 foot 1 12

inches

13 inches = 1083 ft

Example 2 Convert 13 inches into yards

Step 1hellip starting with 13 sohellip 13 in

1

Step 2hellip conversion factors 1 ft 1 yd

12 in 3 ft

Step 3hellip place factors 13 in x 1 ft x 1 yd =

1 12 in 3 ft

Step 4hellip check cancellations 13 in x 1 ft x 1 yd

1 12 in 3 ft

13 in = 036 yd

Example 3 Convert 2 years into seconds

2 yrs x 365 days x 24 h x 60 min x 60 sec

1 1 yr 1 day 1 h 1 min

2 yrs = 63072000 sec

Example 4 Convert 4 decades into minutes

4 dec x 10 yrs x 365 days x 24 h x 60 min

1 1 dec 1 yr 1 day 1 h

4 decades = 21024000 m

Example 5 I am 5rsquo 3rdquo or (5 x 12) + 3 = 63 inches tall How many cm tall am I

63 in x 256 cm =

1 1 in

63 in = 1601 cm

Dimensional Analysis Worksheet

1 In New Jersey students in public schools go to school for 4 years How many minutes are students enrolled in high school

4 years x 365 days x 24 h x 60 min

1 1 yr 1 day 1 h

4 yrs = 2102400 min

2 Alaynarsquos dog is 3 ft tall What is the dogrsquos height in mm

3 ft x 12 in x 254 cm x 10 mm

1 1 ft 1 in 1 cm

3 ft = 9144 mm

3 Brian and Jesse were on a bus trip going 50 MPH For some extra fun they decided to convert the busrsquos speed into kmh What should their answer be

50 miles x 161 km 1 hr 1 mile

50 MPH = 805 kmh

4 Driving home from practice Alexrsquos mother was driving at a speed of 30 ms What was their speed in kmh

30 m x 1 km x 60 s x 60 min 1 s 1000 m 1 min 1 h

30 ms = 108 kmh

5 Saskia was riding her bike down the road at a speed of 5 kmh What was her speed in ms

5 km x 1000 m x 1 hr x 1 min 1 h 1 km 60 min 60 s

5 kmh = 139 ms

Class experiment

1 Determine how tall you are in inches

2 Using the conversion factor 1 mile = 161 km determine how tall you are in cm

3 Check your answer with a meter stick

AccelerationWhen you accelerate what are you doing

Speeding uphellip accelerating

When you slow down what are you doing

Decelerating

In physics we use the same term ldquoaccelerationrdquo for both speeding up and slowing down We distinguish between the two by assigning positive or negative values

+ acceleration as in speeding up positive

- acceleration as in slowing down negative

Acceleration = the change in velocity over time

- measured in ms or ms2

s

Acceleration = ∆ Velocity

∆ Time

Acceleration = ∆ Distance + Direction

∆ Time

∆ Time

Given an object moving in a circle

- ∆ velocity due to a ∆ direction

- if ∆ velocity the ∆ acceleration as well

- circular motion = ∆ D = ∆ V = ∆ A

Graphing Acceleration

A = ∆ V and slope = ∆ Y

∆ T ∆ X

Acceleration = ∆ V = ∆ Y = Slope of line

∆ T ∆ X

So Acceleration = Slope of line

Steep slope = fast movement

Gradual slope = slow movement

Acceleration Deceleration

V

T

V

T

Steepness of the line indicates the degree of acceleration

V

T

V

T

Comparing Velocity and Acceleration

Velocity = ∆ Distance Acceleration = ∆ Velocity

∆ Time ∆ Time

D

T

These two lines indicate the exact same thing the same rate of acceleration

bull Acceleration = + slope

bull Deceleration = - slope

T

V

+ slope

- slope

When object is a rest Velocity is zero

If ∆ Distance = 0 then ∆ Velocityhellip so Acceleration = 0

D

T

V

T

0

When acceleration equals zero

A= ∆ V no change in velocity

∆ T Time will always pass

No change in velocity

- no velocity ndash V = 0 then object is at rest

- constant velocity - ∆ V = Vfinal ndash Vinitial

Vf = 50 milesh and Vi = 50 milesh

Then ∆ V = 0

If acceleration = zero you are either stopped or on cruise control

To determine which you must find if there is a change in distance

How it all fits togetherFrom Motion Acceleration only one variable is

added at a time1 Motion = ∆ Distance2 Speed = ∆ Distance

∆ Time3 Velocity = ∆ Distance + Direction

∆ Time4 Acceleration = ∆ Distance + Direction

∆ Time∆ Time

Momentum

When an object is in motion we think velocity However we must not forget Momentum ndash which is also acting on the object

Momentum = a quantity defined as the product of an objectrsquos mass and its velocity - In a formula P = momentum- momentum moves in the same direction as the velocity

P = Mass x Velocity

- Measured in kgms

Momentum and ∆ Velocity

- large momentum difficult to change velocity

- small momentum easier to change velocity

Class Experiment Red light green light

Stationary objects have momentum of zero

Why No motion = no speed = no velocity = no momentum

Momentum is directly proportional to masshellip momentum increases as mass increases

P

Mass (kg)

Force

Force = the cause of acceleration or a change in velocity

- force is measured in units called Newtons

Net force = the combination of all the forces acting upon an object

bull The size of the arrow represents the amount of forcehellip

bull The arrows are the same so there is no movement

Friction

Friction = the force between two objects in contact that opposes the motion of either object

Pretend you are in a helicopter looking down on a ski slope in early springhellip The ice is meltinghellip Patches of dirt and gravel begin to showhellip

How much friction

Skis + snow = little frictionhellip skis move over snow

Skis + dirt = a lot of frictionhellip skis do not move over dirt

Air resistance is a type of friction

Gravity

Gravity = Force of attraction between 2 objects due to their masses

The force of gravity is different on different planets moons etc

On earth g = 98ms2

Gravity depends upon the masses as well as the distance between objects

Newtonrsquos Laws of Motion

Newtonrsquos 1st Law- the law of inertia

An object at rest remains at rest and an object in motion remains in motion unless it experiences an unbalanced force

bull Example 1 Whiplash ndash Person B is stopped at a traffic light Person A is not paying attention and rear-ends Person B

bull Result Person B moves forward suddenlyhellip Their head snaps back as it attempts to ldquoremain at restrdquo Their body attached to the seat moves forwardhellip their head snaps forward to catch up with the body resulting in whiplash

Example 2 Bus ride - The bus driver does not like children Every time they get too loud he slams on the breaks Why does he do this

Inertia = The tendency of an object to remain at rest or in motion with a constant velocity All objects have inertia because they resist changes in motion

Trivia If two people on a space ship (in space) get into a physical fight which will win

Person A Person B

Even though they are weightlesshellip there is no gravity Person A has a greater mass therefore a greater inertia

Newtonrsquos 2nd law of Motion- the law of acceleration

bull The unbalanced force acting on an object equals the objectrsquos mass times its acceleration

bull Force = Mass x Acceleration

Example pushing a cart

The greater the mass the more force needed to cause acceleration

Bumper cars

bull Series of motions

bull Rest-forward-rest-backward-rest

bull Note does not represent the profile of the terrain

T

D

Velocity Graphs and Profiles of Terrain

bull What do we know about movement

bull 1 ndash rest

bull 2 ndash gradual movement forward

bull 3 ndash rest

bull 4 ndash backward movement

bull 5 ndash rest

1

2

3

4

5

T

D

Velocity Graphs and Profiles of Terrain

bull 1 ndash You are halfway up a hill at rest holding a wagon

bull 2 ndash You start moving uphillbull 3 ndash You take a restbull 4 ndash The wagon handle slips

out of you hand and travels backward down the hill

bull 5 ndash The wagon stops moving at the bottom of the hill

1

2

3

4

5

T

D

bull What could be a possible explanation pulling a wagon uphill

Dimensional Analysis ndash Unit Analysis

In your head you can probably converthellip

hellip inches to feet

sure 12 in = 1 ft

hellip inches to yards

okay 3 ft in 1 yd = 36 in

hellip inches to miles

um probably not

bull FAQ When I convert from inches to yards or yards to inches when do I multiply and when do I divide

bull The easiest way to approach these unit conversions is by using dimensional analysis

There are 4 rules1 If you use only one unit to start put it over a

12 Determine the conversion factors (Ex 12

inches = 1 ft) and put into a fraction3 Properly place the conversion factors in an

equation4 Check cancellations of units so that you are

left with the unit you were looking for on the top of a division bar The units that are canceled should be on opposite sides of the division bar

Example 1 How many feet in 13 in 1 112 or 1083 ftStep 1hellip starting with 13 sohellip 13 inches

1

Step 2hellip conversion factors 1 foot or 12 inches 12 inches 1 foot

Step 3hellip place factors 13 inches x 1 foot 1 12 inches

Step 4hellip check cancellations 13 inches x 1 foot 1 12

inches

13 inches = 1083 ft

Example 2 Convert 13 inches into yards

Step 1hellip starting with 13 sohellip 13 in

1

Step 2hellip conversion factors 1 ft 1 yd

12 in 3 ft

Step 3hellip place factors 13 in x 1 ft x 1 yd =

1 12 in 3 ft

Step 4hellip check cancellations 13 in x 1 ft x 1 yd

1 12 in 3 ft

13 in = 036 yd

Example 3 Convert 2 years into seconds

2 yrs x 365 days x 24 h x 60 min x 60 sec

1 1 yr 1 day 1 h 1 min

2 yrs = 63072000 sec

Example 4 Convert 4 decades into minutes

4 dec x 10 yrs x 365 days x 24 h x 60 min

1 1 dec 1 yr 1 day 1 h

4 decades = 21024000 m

Example 5 I am 5rsquo 3rdquo or (5 x 12) + 3 = 63 inches tall How many cm tall am I

63 in x 256 cm =

1 1 in

63 in = 1601 cm

Dimensional Analysis Worksheet

1 In New Jersey students in public schools go to school for 4 years How many minutes are students enrolled in high school

4 years x 365 days x 24 h x 60 min

1 1 yr 1 day 1 h

4 yrs = 2102400 min

2 Alaynarsquos dog is 3 ft tall What is the dogrsquos height in mm

3 ft x 12 in x 254 cm x 10 mm

1 1 ft 1 in 1 cm

3 ft = 9144 mm

3 Brian and Jesse were on a bus trip going 50 MPH For some extra fun they decided to convert the busrsquos speed into kmh What should their answer be

50 miles x 161 km 1 hr 1 mile

50 MPH = 805 kmh

4 Driving home from practice Alexrsquos mother was driving at a speed of 30 ms What was their speed in kmh

30 m x 1 km x 60 s x 60 min 1 s 1000 m 1 min 1 h

30 ms = 108 kmh

5 Saskia was riding her bike down the road at a speed of 5 kmh What was her speed in ms

5 km x 1000 m x 1 hr x 1 min 1 h 1 km 60 min 60 s

5 kmh = 139 ms

Class experiment

1 Determine how tall you are in inches

2 Using the conversion factor 1 mile = 161 km determine how tall you are in cm

3 Check your answer with a meter stick

AccelerationWhen you accelerate what are you doing

Speeding uphellip accelerating

When you slow down what are you doing

Decelerating

In physics we use the same term ldquoaccelerationrdquo for both speeding up and slowing down We distinguish between the two by assigning positive or negative values

+ acceleration as in speeding up positive

- acceleration as in slowing down negative

Acceleration = the change in velocity over time

- measured in ms or ms2

s

Acceleration = ∆ Velocity

∆ Time

Acceleration = ∆ Distance + Direction

∆ Time

∆ Time

Given an object moving in a circle

- ∆ velocity due to a ∆ direction

- if ∆ velocity the ∆ acceleration as well

- circular motion = ∆ D = ∆ V = ∆ A

Graphing Acceleration

A = ∆ V and slope = ∆ Y

∆ T ∆ X

Acceleration = ∆ V = ∆ Y = Slope of line

∆ T ∆ X

So Acceleration = Slope of line

Steep slope = fast movement

Gradual slope = slow movement

Acceleration Deceleration

V

T

V

T

Steepness of the line indicates the degree of acceleration

V

T

V

T

Comparing Velocity and Acceleration

Velocity = ∆ Distance Acceleration = ∆ Velocity

∆ Time ∆ Time

D

T

These two lines indicate the exact same thing the same rate of acceleration

bull Acceleration = + slope

bull Deceleration = - slope

T

V

+ slope

- slope

When object is a rest Velocity is zero

If ∆ Distance = 0 then ∆ Velocityhellip so Acceleration = 0

D

T

V

T

0

When acceleration equals zero

A= ∆ V no change in velocity

∆ T Time will always pass

No change in velocity

- no velocity ndash V = 0 then object is at rest

- constant velocity - ∆ V = Vfinal ndash Vinitial

Vf = 50 milesh and Vi = 50 milesh

Then ∆ V = 0

If acceleration = zero you are either stopped or on cruise control

To determine which you must find if there is a change in distance

How it all fits togetherFrom Motion Acceleration only one variable is

added at a time1 Motion = ∆ Distance2 Speed = ∆ Distance

∆ Time3 Velocity = ∆ Distance + Direction

∆ Time4 Acceleration = ∆ Distance + Direction

∆ Time∆ Time

Momentum

When an object is in motion we think velocity However we must not forget Momentum ndash which is also acting on the object

Momentum = a quantity defined as the product of an objectrsquos mass and its velocity - In a formula P = momentum- momentum moves in the same direction as the velocity

P = Mass x Velocity

- Measured in kgms

Momentum and ∆ Velocity

- large momentum difficult to change velocity

- small momentum easier to change velocity

Class Experiment Red light green light

Stationary objects have momentum of zero

Why No motion = no speed = no velocity = no momentum

Momentum is directly proportional to masshellip momentum increases as mass increases

P

Mass (kg)

Force

Force = the cause of acceleration or a change in velocity

- force is measured in units called Newtons

Net force = the combination of all the forces acting upon an object

bull The size of the arrow represents the amount of forcehellip

bull The arrows are the same so there is no movement

Friction

Friction = the force between two objects in contact that opposes the motion of either object

Pretend you are in a helicopter looking down on a ski slope in early springhellip The ice is meltinghellip Patches of dirt and gravel begin to showhellip

How much friction

Skis + snow = little frictionhellip skis move over snow

Skis + dirt = a lot of frictionhellip skis do not move over dirt

Air resistance is a type of friction

Gravity

Gravity = Force of attraction between 2 objects due to their masses

The force of gravity is different on different planets moons etc

On earth g = 98ms2

Gravity depends upon the masses as well as the distance between objects

Newtonrsquos Laws of Motion

Newtonrsquos 1st Law- the law of inertia

An object at rest remains at rest and an object in motion remains in motion unless it experiences an unbalanced force

bull Example 1 Whiplash ndash Person B is stopped at a traffic light Person A is not paying attention and rear-ends Person B

bull Result Person B moves forward suddenlyhellip Their head snaps back as it attempts to ldquoremain at restrdquo Their body attached to the seat moves forwardhellip their head snaps forward to catch up with the body resulting in whiplash

Example 2 Bus ride - The bus driver does not like children Every time they get too loud he slams on the breaks Why does he do this

Inertia = The tendency of an object to remain at rest or in motion with a constant velocity All objects have inertia because they resist changes in motion

Trivia If two people on a space ship (in space) get into a physical fight which will win

Person A Person B

Even though they are weightlesshellip there is no gravity Person A has a greater mass therefore a greater inertia

Newtonrsquos 2nd law of Motion- the law of acceleration

bull The unbalanced force acting on an object equals the objectrsquos mass times its acceleration

bull Force = Mass x Acceleration

Example pushing a cart

The greater the mass the more force needed to cause acceleration

Bumper cars

Velocity Graphs and Profiles of Terrain

bull What do we know about movement

bull 1 ndash rest

bull 2 ndash gradual movement forward

bull 3 ndash rest

bull 4 ndash backward movement

bull 5 ndash rest

1

2

3

4

5

T

D

Velocity Graphs and Profiles of Terrain

bull 1 ndash You are halfway up a hill at rest holding a wagon

bull 2 ndash You start moving uphillbull 3 ndash You take a restbull 4 ndash The wagon handle slips

out of you hand and travels backward down the hill

bull 5 ndash The wagon stops moving at the bottom of the hill

1

2

3

4

5

T

D

bull What could be a possible explanation pulling a wagon uphill

Dimensional Analysis ndash Unit Analysis

In your head you can probably converthellip

hellip inches to feet

sure 12 in = 1 ft

hellip inches to yards

okay 3 ft in 1 yd = 36 in

hellip inches to miles

um probably not

bull FAQ When I convert from inches to yards or yards to inches when do I multiply and when do I divide

bull The easiest way to approach these unit conversions is by using dimensional analysis

There are 4 rules1 If you use only one unit to start put it over a

12 Determine the conversion factors (Ex 12

inches = 1 ft) and put into a fraction3 Properly place the conversion factors in an

equation4 Check cancellations of units so that you are

left with the unit you were looking for on the top of a division bar The units that are canceled should be on opposite sides of the division bar

Example 1 How many feet in 13 in 1 112 or 1083 ftStep 1hellip starting with 13 sohellip 13 inches

1

Step 2hellip conversion factors 1 foot or 12 inches 12 inches 1 foot

Step 3hellip place factors 13 inches x 1 foot 1 12 inches

Step 4hellip check cancellations 13 inches x 1 foot 1 12

inches

13 inches = 1083 ft

Example 2 Convert 13 inches into yards

Step 1hellip starting with 13 sohellip 13 in

1

Step 2hellip conversion factors 1 ft 1 yd

12 in 3 ft

Step 3hellip place factors 13 in x 1 ft x 1 yd =

1 12 in 3 ft

Step 4hellip check cancellations 13 in x 1 ft x 1 yd

1 12 in 3 ft

13 in = 036 yd

Example 3 Convert 2 years into seconds

2 yrs x 365 days x 24 h x 60 min x 60 sec

1 1 yr 1 day 1 h 1 min

2 yrs = 63072000 sec

Example 4 Convert 4 decades into minutes

4 dec x 10 yrs x 365 days x 24 h x 60 min

1 1 dec 1 yr 1 day 1 h

4 decades = 21024000 m

Example 5 I am 5rsquo 3rdquo or (5 x 12) + 3 = 63 inches tall How many cm tall am I

63 in x 256 cm =

1 1 in

63 in = 1601 cm

Dimensional Analysis Worksheet

1 In New Jersey students in public schools go to school for 4 years How many minutes are students enrolled in high school

4 years x 365 days x 24 h x 60 min

1 1 yr 1 day 1 h

4 yrs = 2102400 min

2 Alaynarsquos dog is 3 ft tall What is the dogrsquos height in mm

3 ft x 12 in x 254 cm x 10 mm

1 1 ft 1 in 1 cm

3 ft = 9144 mm

3 Brian and Jesse were on a bus trip going 50 MPH For some extra fun they decided to convert the busrsquos speed into kmh What should their answer be

50 miles x 161 km 1 hr 1 mile

50 MPH = 805 kmh

4 Driving home from practice Alexrsquos mother was driving at a speed of 30 ms What was their speed in kmh

30 m x 1 km x 60 s x 60 min 1 s 1000 m 1 min 1 h

30 ms = 108 kmh

5 Saskia was riding her bike down the road at a speed of 5 kmh What was her speed in ms

5 km x 1000 m x 1 hr x 1 min 1 h 1 km 60 min 60 s

5 kmh = 139 ms

Class experiment

1 Determine how tall you are in inches

2 Using the conversion factor 1 mile = 161 km determine how tall you are in cm

3 Check your answer with a meter stick

AccelerationWhen you accelerate what are you doing

Speeding uphellip accelerating

When you slow down what are you doing

Decelerating

In physics we use the same term ldquoaccelerationrdquo for both speeding up and slowing down We distinguish between the two by assigning positive or negative values

+ acceleration as in speeding up positive

- acceleration as in slowing down negative

Acceleration = the change in velocity over time

- measured in ms or ms2

s

Acceleration = ∆ Velocity

∆ Time

Acceleration = ∆ Distance + Direction

∆ Time

∆ Time

Given an object moving in a circle

- ∆ velocity due to a ∆ direction

- if ∆ velocity the ∆ acceleration as well

- circular motion = ∆ D = ∆ V = ∆ A

Graphing Acceleration

A = ∆ V and slope = ∆ Y

∆ T ∆ X

Acceleration = ∆ V = ∆ Y = Slope of line

∆ T ∆ X

So Acceleration = Slope of line

Steep slope = fast movement

Gradual slope = slow movement

Acceleration Deceleration

V

T

V

T

Steepness of the line indicates the degree of acceleration

V

T

V

T

Comparing Velocity and Acceleration

Velocity = ∆ Distance Acceleration = ∆ Velocity

∆ Time ∆ Time

D

T

These two lines indicate the exact same thing the same rate of acceleration

bull Acceleration = + slope

bull Deceleration = - slope

T

V

+ slope

- slope

When object is a rest Velocity is zero

If ∆ Distance = 0 then ∆ Velocityhellip so Acceleration = 0

D

T

V

T

0

When acceleration equals zero

A= ∆ V no change in velocity

∆ T Time will always pass

No change in velocity

- no velocity ndash V = 0 then object is at rest

- constant velocity - ∆ V = Vfinal ndash Vinitial

Vf = 50 milesh and Vi = 50 milesh

Then ∆ V = 0

If acceleration = zero you are either stopped or on cruise control

To determine which you must find if there is a change in distance

How it all fits togetherFrom Motion Acceleration only one variable is

added at a time1 Motion = ∆ Distance2 Speed = ∆ Distance

∆ Time3 Velocity = ∆ Distance + Direction

∆ Time4 Acceleration = ∆ Distance + Direction

∆ Time∆ Time

Momentum

When an object is in motion we think velocity However we must not forget Momentum ndash which is also acting on the object

Momentum = a quantity defined as the product of an objectrsquos mass and its velocity - In a formula P = momentum- momentum moves in the same direction as the velocity

P = Mass x Velocity

- Measured in kgms

Momentum and ∆ Velocity

- large momentum difficult to change velocity

- small momentum easier to change velocity

Class Experiment Red light green light

Stationary objects have momentum of zero

Why No motion = no speed = no velocity = no momentum

Momentum is directly proportional to masshellip momentum increases as mass increases

P

Mass (kg)

Force

Force = the cause of acceleration or a change in velocity

- force is measured in units called Newtons

Net force = the combination of all the forces acting upon an object

bull The size of the arrow represents the amount of forcehellip

bull The arrows are the same so there is no movement

Friction

Friction = the force between two objects in contact that opposes the motion of either object

Pretend you are in a helicopter looking down on a ski slope in early springhellip The ice is meltinghellip Patches of dirt and gravel begin to showhellip

How much friction

Skis + snow = little frictionhellip skis move over snow

Skis + dirt = a lot of frictionhellip skis do not move over dirt

Air resistance is a type of friction

Gravity

Gravity = Force of attraction between 2 objects due to their masses

The force of gravity is different on different planets moons etc

On earth g = 98ms2

Gravity depends upon the masses as well as the distance between objects

Newtonrsquos Laws of Motion

Newtonrsquos 1st Law- the law of inertia

An object at rest remains at rest and an object in motion remains in motion unless it experiences an unbalanced force

bull Example 1 Whiplash ndash Person B is stopped at a traffic light Person A is not paying attention and rear-ends Person B

bull Result Person B moves forward suddenlyhellip Their head snaps back as it attempts to ldquoremain at restrdquo Their body attached to the seat moves forwardhellip their head snaps forward to catch up with the body resulting in whiplash

Example 2 Bus ride - The bus driver does not like children Every time they get too loud he slams on the breaks Why does he do this

Inertia = The tendency of an object to remain at rest or in motion with a constant velocity All objects have inertia because they resist changes in motion

Trivia If two people on a space ship (in space) get into a physical fight which will win

Person A Person B

Even though they are weightlesshellip there is no gravity Person A has a greater mass therefore a greater inertia

Newtonrsquos 2nd law of Motion- the law of acceleration

bull The unbalanced force acting on an object equals the objectrsquos mass times its acceleration

bull Force = Mass x Acceleration

Example pushing a cart

The greater the mass the more force needed to cause acceleration

Bumper cars

Velocity Graphs and Profiles of Terrain

bull 1 ndash You are halfway up a hill at rest holding a wagon

bull 2 ndash You start moving uphillbull 3 ndash You take a restbull 4 ndash The wagon handle slips

out of you hand and travels backward down the hill

bull 5 ndash The wagon stops moving at the bottom of the hill

1

2

3

4

5

T

D

bull What could be a possible explanation pulling a wagon uphill

Dimensional Analysis ndash Unit Analysis

In your head you can probably converthellip

hellip inches to feet

sure 12 in = 1 ft

hellip inches to yards

okay 3 ft in 1 yd = 36 in

hellip inches to miles

um probably not

bull FAQ When I convert from inches to yards or yards to inches when do I multiply and when do I divide

bull The easiest way to approach these unit conversions is by using dimensional analysis

There are 4 rules1 If you use only one unit to start put it over a

12 Determine the conversion factors (Ex 12

inches = 1 ft) and put into a fraction3 Properly place the conversion factors in an

equation4 Check cancellations of units so that you are

left with the unit you were looking for on the top of a division bar The units that are canceled should be on opposite sides of the division bar

Example 1 How many feet in 13 in 1 112 or 1083 ftStep 1hellip starting with 13 sohellip 13 inches

1

Step 2hellip conversion factors 1 foot or 12 inches 12 inches 1 foot

Step 3hellip place factors 13 inches x 1 foot 1 12 inches

Step 4hellip check cancellations 13 inches x 1 foot 1 12

inches

13 inches = 1083 ft

Example 2 Convert 13 inches into yards

Step 1hellip starting with 13 sohellip 13 in

1

Step 2hellip conversion factors 1 ft 1 yd

12 in 3 ft

Step 3hellip place factors 13 in x 1 ft x 1 yd =

1 12 in 3 ft

Step 4hellip check cancellations 13 in x 1 ft x 1 yd

1 12 in 3 ft

13 in = 036 yd

Example 3 Convert 2 years into seconds

2 yrs x 365 days x 24 h x 60 min x 60 sec

1 1 yr 1 day 1 h 1 min

2 yrs = 63072000 sec

Example 4 Convert 4 decades into minutes

4 dec x 10 yrs x 365 days x 24 h x 60 min

1 1 dec 1 yr 1 day 1 h

4 decades = 21024000 m

Example 5 I am 5rsquo 3rdquo or (5 x 12) + 3 = 63 inches tall How many cm tall am I

63 in x 256 cm =

1 1 in

63 in = 1601 cm

Dimensional Analysis Worksheet

1 In New Jersey students in public schools go to school for 4 years How many minutes are students enrolled in high school

4 years x 365 days x 24 h x 60 min

1 1 yr 1 day 1 h

4 yrs = 2102400 min

2 Alaynarsquos dog is 3 ft tall What is the dogrsquos height in mm

3 ft x 12 in x 254 cm x 10 mm

1 1 ft 1 in 1 cm

3 ft = 9144 mm

3 Brian and Jesse were on a bus trip going 50 MPH For some extra fun they decided to convert the busrsquos speed into kmh What should their answer be

50 miles x 161 km 1 hr 1 mile

50 MPH = 805 kmh

4 Driving home from practice Alexrsquos mother was driving at a speed of 30 ms What was their speed in kmh

30 m x 1 km x 60 s x 60 min 1 s 1000 m 1 min 1 h

30 ms = 108 kmh

5 Saskia was riding her bike down the road at a speed of 5 kmh What was her speed in ms

5 km x 1000 m x 1 hr x 1 min 1 h 1 km 60 min 60 s

5 kmh = 139 ms

Class experiment

1 Determine how tall you are in inches

2 Using the conversion factor 1 mile = 161 km determine how tall you are in cm

3 Check your answer with a meter stick

AccelerationWhen you accelerate what are you doing

Speeding uphellip accelerating

When you slow down what are you doing

Decelerating

In physics we use the same term ldquoaccelerationrdquo for both speeding up and slowing down We distinguish between the two by assigning positive or negative values

+ acceleration as in speeding up positive

- acceleration as in slowing down negative

Acceleration = the change in velocity over time

- measured in ms or ms2

s

Acceleration = ∆ Velocity

∆ Time

Acceleration = ∆ Distance + Direction

∆ Time

∆ Time

Given an object moving in a circle

- ∆ velocity due to a ∆ direction

- if ∆ velocity the ∆ acceleration as well

- circular motion = ∆ D = ∆ V = ∆ A

Graphing Acceleration

A = ∆ V and slope = ∆ Y

∆ T ∆ X

Acceleration = ∆ V = ∆ Y = Slope of line

∆ T ∆ X

So Acceleration = Slope of line

Steep slope = fast movement

Gradual slope = slow movement

Acceleration Deceleration

V

T

V

T

Steepness of the line indicates the degree of acceleration

V

T

V

T

Comparing Velocity and Acceleration

Velocity = ∆ Distance Acceleration = ∆ Velocity

∆ Time ∆ Time

D

T

These two lines indicate the exact same thing the same rate of acceleration

bull Acceleration = + slope

bull Deceleration = - slope

T

V

+ slope

- slope

When object is a rest Velocity is zero

If ∆ Distance = 0 then ∆ Velocityhellip so Acceleration = 0

D

T

V

T

0

When acceleration equals zero

A= ∆ V no change in velocity

∆ T Time will always pass

No change in velocity

- no velocity ndash V = 0 then object is at rest

- constant velocity - ∆ V = Vfinal ndash Vinitial

Vf = 50 milesh and Vi = 50 milesh

Then ∆ V = 0

If acceleration = zero you are either stopped or on cruise control

To determine which you must find if there is a change in distance

How it all fits togetherFrom Motion Acceleration only one variable is

added at a time1 Motion = ∆ Distance2 Speed = ∆ Distance

∆ Time3 Velocity = ∆ Distance + Direction

∆ Time4 Acceleration = ∆ Distance + Direction

∆ Time∆ Time

Momentum

When an object is in motion we think velocity However we must not forget Momentum ndash which is also acting on the object

Momentum = a quantity defined as the product of an objectrsquos mass and its velocity - In a formula P = momentum- momentum moves in the same direction as the velocity

P = Mass x Velocity

- Measured in kgms

Momentum and ∆ Velocity

- large momentum difficult to change velocity

- small momentum easier to change velocity

Class Experiment Red light green light

Stationary objects have momentum of zero

Why No motion = no speed = no velocity = no momentum

Momentum is directly proportional to masshellip momentum increases as mass increases

P

Mass (kg)

Force

Force = the cause of acceleration or a change in velocity

- force is measured in units called Newtons

Net force = the combination of all the forces acting upon an object

bull The size of the arrow represents the amount of forcehellip

bull The arrows are the same so there is no movement

Friction

Friction = the force between two objects in contact that opposes the motion of either object

Pretend you are in a helicopter looking down on a ski slope in early springhellip The ice is meltinghellip Patches of dirt and gravel begin to showhellip

How much friction

Skis + snow = little frictionhellip skis move over snow

Skis + dirt = a lot of frictionhellip skis do not move over dirt

Air resistance is a type of friction

Gravity

Gravity = Force of attraction between 2 objects due to their masses

The force of gravity is different on different planets moons etc

On earth g = 98ms2

Gravity depends upon the masses as well as the distance between objects

Newtonrsquos Laws of Motion

Newtonrsquos 1st Law- the law of inertia

An object at rest remains at rest and an object in motion remains in motion unless it experiences an unbalanced force

bull Example 1 Whiplash ndash Person B is stopped at a traffic light Person A is not paying attention and rear-ends Person B

bull Result Person B moves forward suddenlyhellip Their head snaps back as it attempts to ldquoremain at restrdquo Their body attached to the seat moves forwardhellip their head snaps forward to catch up with the body resulting in whiplash

Example 2 Bus ride - The bus driver does not like children Every time they get too loud he slams on the breaks Why does he do this

Inertia = The tendency of an object to remain at rest or in motion with a constant velocity All objects have inertia because they resist changes in motion

Trivia If two people on a space ship (in space) get into a physical fight which will win

Person A Person B

Even though they are weightlesshellip there is no gravity Person A has a greater mass therefore a greater inertia

Newtonrsquos 2nd law of Motion- the law of acceleration

bull The unbalanced force acting on an object equals the objectrsquos mass times its acceleration

bull Force = Mass x Acceleration

Example pushing a cart

The greater the mass the more force needed to cause acceleration

Bumper cars

Dimensional Analysis ndash Unit Analysis

In your head you can probably converthellip

hellip inches to feet

sure 12 in = 1 ft

hellip inches to yards

okay 3 ft in 1 yd = 36 in

hellip inches to miles

um probably not

bull FAQ When I convert from inches to yards or yards to inches when do I multiply and when do I divide

bull The easiest way to approach these unit conversions is by using dimensional analysis

There are 4 rules1 If you use only one unit to start put it over a

12 Determine the conversion factors (Ex 12

inches = 1 ft) and put into a fraction3 Properly place the conversion factors in an

equation4 Check cancellations of units so that you are

left with the unit you were looking for on the top of a division bar The units that are canceled should be on opposite sides of the division bar

Example 1 How many feet in 13 in 1 112 or 1083 ftStep 1hellip starting with 13 sohellip 13 inches

1

Step 2hellip conversion factors 1 foot or 12 inches 12 inches 1 foot

Step 3hellip place factors 13 inches x 1 foot 1 12 inches

Step 4hellip check cancellations 13 inches x 1 foot 1 12

inches

13 inches = 1083 ft

Example 2 Convert 13 inches into yards

Step 1hellip starting with 13 sohellip 13 in

1

Step 2hellip conversion factors 1 ft 1 yd

12 in 3 ft

Step 3hellip place factors 13 in x 1 ft x 1 yd =

1 12 in 3 ft

Step 4hellip check cancellations 13 in x 1 ft x 1 yd

1 12 in 3 ft

13 in = 036 yd

Example 3 Convert 2 years into seconds

2 yrs x 365 days x 24 h x 60 min x 60 sec

1 1 yr 1 day 1 h 1 min

2 yrs = 63072000 sec

Example 4 Convert 4 decades into minutes

4 dec x 10 yrs x 365 days x 24 h x 60 min

1 1 dec 1 yr 1 day 1 h

4 decades = 21024000 m

Example 5 I am 5rsquo 3rdquo or (5 x 12) + 3 = 63 inches tall How many cm tall am I

63 in x 256 cm =

1 1 in

63 in = 1601 cm

Dimensional Analysis Worksheet

1 In New Jersey students in public schools go to school for 4 years How many minutes are students enrolled in high school

4 years x 365 days x 24 h x 60 min

1 1 yr 1 day 1 h

4 yrs = 2102400 min

2 Alaynarsquos dog is 3 ft tall What is the dogrsquos height in mm

3 ft x 12 in x 254 cm x 10 mm

1 1 ft 1 in 1 cm

3 ft = 9144 mm

3 Brian and Jesse were on a bus trip going 50 MPH For some extra fun they decided to convert the busrsquos speed into kmh What should their answer be

50 miles x 161 km 1 hr 1 mile

50 MPH = 805 kmh

4 Driving home from practice Alexrsquos mother was driving at a speed of 30 ms What was their speed in kmh

30 m x 1 km x 60 s x 60 min 1 s 1000 m 1 min 1 h

30 ms = 108 kmh

5 Saskia was riding her bike down the road at a speed of 5 kmh What was her speed in ms

5 km x 1000 m x 1 hr x 1 min 1 h 1 km 60 min 60 s

5 kmh = 139 ms

Class experiment

1 Determine how tall you are in inches

2 Using the conversion factor 1 mile = 161 km determine how tall you are in cm

3 Check your answer with a meter stick

AccelerationWhen you accelerate what are you doing

Speeding uphellip accelerating

When you slow down what are you doing

Decelerating

In physics we use the same term ldquoaccelerationrdquo for both speeding up and slowing down We distinguish between the two by assigning positive or negative values

+ acceleration as in speeding up positive

- acceleration as in slowing down negative

Acceleration = the change in velocity over time

- measured in ms or ms2

s

Acceleration = ∆ Velocity

∆ Time

Acceleration = ∆ Distance + Direction

∆ Time

∆ Time

Given an object moving in a circle

- ∆ velocity due to a ∆ direction

- if ∆ velocity the ∆ acceleration as well

- circular motion = ∆ D = ∆ V = ∆ A

Graphing Acceleration

A = ∆ V and slope = ∆ Y

∆ T ∆ X

Acceleration = ∆ V = ∆ Y = Slope of line

∆ T ∆ X

So Acceleration = Slope of line

Steep slope = fast movement

Gradual slope = slow movement

Acceleration Deceleration

V

T

V

T

Steepness of the line indicates the degree of acceleration

V

T

V

T

Comparing Velocity and Acceleration

Velocity = ∆ Distance Acceleration = ∆ Velocity

∆ Time ∆ Time

D

T

These two lines indicate the exact same thing the same rate of acceleration

bull Acceleration = + slope

bull Deceleration = - slope

T

V

+ slope

- slope

When object is a rest Velocity is zero

If ∆ Distance = 0 then ∆ Velocityhellip so Acceleration = 0

D

T

V

T

0

When acceleration equals zero

A= ∆ V no change in velocity

∆ T Time will always pass

No change in velocity

- no velocity ndash V = 0 then object is at rest

- constant velocity - ∆ V = Vfinal ndash Vinitial

Vf = 50 milesh and Vi = 50 milesh

Then ∆ V = 0

If acceleration = zero you are either stopped or on cruise control

To determine which you must find if there is a change in distance

How it all fits togetherFrom Motion Acceleration only one variable is

added at a time1 Motion = ∆ Distance2 Speed = ∆ Distance

∆ Time3 Velocity = ∆ Distance + Direction

∆ Time4 Acceleration = ∆ Distance + Direction

∆ Time∆ Time

Momentum

When an object is in motion we think velocity However we must not forget Momentum ndash which is also acting on the object

Momentum = a quantity defined as the product of an objectrsquos mass and its velocity - In a formula P = momentum- momentum moves in the same direction as the velocity

P = Mass x Velocity

- Measured in kgms

Momentum and ∆ Velocity

- large momentum difficult to change velocity

- small momentum easier to change velocity

Class Experiment Red light green light

Stationary objects have momentum of zero

Why No motion = no speed = no velocity = no momentum

Momentum is directly proportional to masshellip momentum increases as mass increases

P

Mass (kg)

Force

Force = the cause of acceleration or a change in velocity

- force is measured in units called Newtons

Net force = the combination of all the forces acting upon an object

bull The size of the arrow represents the amount of forcehellip

bull The arrows are the same so there is no movement

Friction

Friction = the force between two objects in contact that opposes the motion of either object

Pretend you are in a helicopter looking down on a ski slope in early springhellip The ice is meltinghellip Patches of dirt and gravel begin to showhellip

How much friction

Skis + snow = little frictionhellip skis move over snow

Skis + dirt = a lot of frictionhellip skis do not move over dirt

Air resistance is a type of friction

Gravity

Gravity = Force of attraction between 2 objects due to their masses

The force of gravity is different on different planets moons etc

On earth g = 98ms2

Gravity depends upon the masses as well as the distance between objects

Newtonrsquos Laws of Motion

Newtonrsquos 1st Law- the law of inertia

An object at rest remains at rest and an object in motion remains in motion unless it experiences an unbalanced force

bull Example 1 Whiplash ndash Person B is stopped at a traffic light Person A is not paying attention and rear-ends Person B

bull Result Person B moves forward suddenlyhellip Their head snaps back as it attempts to ldquoremain at restrdquo Their body attached to the seat moves forwardhellip their head snaps forward to catch up with the body resulting in whiplash

Example 2 Bus ride - The bus driver does not like children Every time they get too loud he slams on the breaks Why does he do this

Inertia = The tendency of an object to remain at rest or in motion with a constant velocity All objects have inertia because they resist changes in motion

Trivia If two people on a space ship (in space) get into a physical fight which will win

Person A Person B

Even though they are weightlesshellip there is no gravity Person A has a greater mass therefore a greater inertia

Newtonrsquos 2nd law of Motion- the law of acceleration

bull The unbalanced force acting on an object equals the objectrsquos mass times its acceleration

bull Force = Mass x Acceleration

Example pushing a cart

The greater the mass the more force needed to cause acceleration

Bumper cars

bull FAQ When I convert from inches to yards or yards to inches when do I multiply and when do I divide

bull The easiest way to approach these unit conversions is by using dimensional analysis

There are 4 rules1 If you use only one unit to start put it over a

12 Determine the conversion factors (Ex 12

inches = 1 ft) and put into a fraction3 Properly place the conversion factors in an

equation4 Check cancellations of units so that you are

left with the unit you were looking for on the top of a division bar The units that are canceled should be on opposite sides of the division bar

Example 1 How many feet in 13 in 1 112 or 1083 ftStep 1hellip starting with 13 sohellip 13 inches

1

Step 2hellip conversion factors 1 foot or 12 inches 12 inches 1 foot

Step 3hellip place factors 13 inches x 1 foot 1 12 inches

Step 4hellip check cancellations 13 inches x 1 foot 1 12

inches

13 inches = 1083 ft

Example 2 Convert 13 inches into yards

Step 1hellip starting with 13 sohellip 13 in

1

Step 2hellip conversion factors 1 ft 1 yd

12 in 3 ft

Step 3hellip place factors 13 in x 1 ft x 1 yd =

1 12 in 3 ft

Step 4hellip check cancellations 13 in x 1 ft x 1 yd

1 12 in 3 ft

13 in = 036 yd

Example 3 Convert 2 years into seconds

2 yrs x 365 days x 24 h x 60 min x 60 sec

1 1 yr 1 day 1 h 1 min

2 yrs = 63072000 sec

Example 4 Convert 4 decades into minutes

4 dec x 10 yrs x 365 days x 24 h x 60 min

1 1 dec 1 yr 1 day 1 h

4 decades = 21024000 m

Example 5 I am 5rsquo 3rdquo or (5 x 12) + 3 = 63 inches tall How many cm tall am I

63 in x 256 cm =

1 1 in

63 in = 1601 cm

Dimensional Analysis Worksheet

1 In New Jersey students in public schools go to school for 4 years How many minutes are students enrolled in high school

4 years x 365 days x 24 h x 60 min

1 1 yr 1 day 1 h

4 yrs = 2102400 min

2 Alaynarsquos dog is 3 ft tall What is the dogrsquos height in mm

3 ft x 12 in x 254 cm x 10 mm

1 1 ft 1 in 1 cm

3 ft = 9144 mm

3 Brian and Jesse were on a bus trip going 50 MPH For some extra fun they decided to convert the busrsquos speed into kmh What should their answer be

50 miles x 161 km 1 hr 1 mile

50 MPH = 805 kmh

4 Driving home from practice Alexrsquos mother was driving at a speed of 30 ms What was their speed in kmh

30 m x 1 km x 60 s x 60 min 1 s 1000 m 1 min 1 h

30 ms = 108 kmh

5 Saskia was riding her bike down the road at a speed of 5 kmh What was her speed in ms

5 km x 1000 m x 1 hr x 1 min 1 h 1 km 60 min 60 s

5 kmh = 139 ms

Class experiment

1 Determine how tall you are in inches

2 Using the conversion factor 1 mile = 161 km determine how tall you are in cm

3 Check your answer with a meter stick

AccelerationWhen you accelerate what are you doing

Speeding uphellip accelerating

When you slow down what are you doing

Decelerating

In physics we use the same term ldquoaccelerationrdquo for both speeding up and slowing down We distinguish between the two by assigning positive or negative values

+ acceleration as in speeding up positive

- acceleration as in slowing down negative

Acceleration = the change in velocity over time

- measured in ms or ms2

s

Acceleration = ∆ Velocity

∆ Time

Acceleration = ∆ Distance + Direction

∆ Time

∆ Time

Given an object moving in a circle

- ∆ velocity due to a ∆ direction

- if ∆ velocity the ∆ acceleration as well

- circular motion = ∆ D = ∆ V = ∆ A

Graphing Acceleration

A = ∆ V and slope = ∆ Y

∆ T ∆ X

Acceleration = ∆ V = ∆ Y = Slope of line

∆ T ∆ X

So Acceleration = Slope of line

Steep slope = fast movement

Gradual slope = slow movement

Acceleration Deceleration

V

T

V

T

Steepness of the line indicates the degree of acceleration

V

T

V

T

Comparing Velocity and Acceleration

Velocity = ∆ Distance Acceleration = ∆ Velocity

∆ Time ∆ Time

D

T

These two lines indicate the exact same thing the same rate of acceleration

bull Acceleration = + slope

bull Deceleration = - slope

T

V

+ slope

- slope

When object is a rest Velocity is zero

If ∆ Distance = 0 then ∆ Velocityhellip so Acceleration = 0

D

T

V

T

0

When acceleration equals zero

A= ∆ V no change in velocity

∆ T Time will always pass

No change in velocity

- no velocity ndash V = 0 then object is at rest

- constant velocity - ∆ V = Vfinal ndash Vinitial

Vf = 50 milesh and Vi = 50 milesh

Then ∆ V = 0

If acceleration = zero you are either stopped or on cruise control

To determine which you must find if there is a change in distance

How it all fits togetherFrom Motion Acceleration only one variable is

added at a time1 Motion = ∆ Distance2 Speed = ∆ Distance

∆ Time3 Velocity = ∆ Distance + Direction

∆ Time4 Acceleration = ∆ Distance + Direction

∆ Time∆ Time

Momentum

When an object is in motion we think velocity However we must not forget Momentum ndash which is also acting on the object

Momentum = a quantity defined as the product of an objectrsquos mass and its velocity - In a formula P = momentum- momentum moves in the same direction as the velocity

P = Mass x Velocity

- Measured in kgms

Momentum and ∆ Velocity

- large momentum difficult to change velocity

- small momentum easier to change velocity

Class Experiment Red light green light

Stationary objects have momentum of zero

Why No motion = no speed = no velocity = no momentum

Momentum is directly proportional to masshellip momentum increases as mass increases

P

Mass (kg)

Force

Force = the cause of acceleration or a change in velocity

- force is measured in units called Newtons

Net force = the combination of all the forces acting upon an object

bull The size of the arrow represents the amount of forcehellip

bull The arrows are the same so there is no movement

Friction

Friction = the force between two objects in contact that opposes the motion of either object

Pretend you are in a helicopter looking down on a ski slope in early springhellip The ice is meltinghellip Patches of dirt and gravel begin to showhellip

How much friction

Skis + snow = little frictionhellip skis move over snow

Skis + dirt = a lot of frictionhellip skis do not move over dirt

Air resistance is a type of friction

Gravity

Gravity = Force of attraction between 2 objects due to their masses

The force of gravity is different on different planets moons etc

On earth g = 98ms2

Gravity depends upon the masses as well as the distance between objects

Newtonrsquos Laws of Motion

Newtonrsquos 1st Law- the law of inertia

An object at rest remains at rest and an object in motion remains in motion unless it experiences an unbalanced force

bull Example 1 Whiplash ndash Person B is stopped at a traffic light Person A is not paying attention and rear-ends Person B

bull Result Person B moves forward suddenlyhellip Their head snaps back as it attempts to ldquoremain at restrdquo Their body attached to the seat moves forwardhellip their head snaps forward to catch up with the body resulting in whiplash

Example 2 Bus ride - The bus driver does not like children Every time they get too loud he slams on the breaks Why does he do this

Inertia = The tendency of an object to remain at rest or in motion with a constant velocity All objects have inertia because they resist changes in motion

Trivia If two people on a space ship (in space) get into a physical fight which will win

Person A Person B

Even though they are weightlesshellip there is no gravity Person A has a greater mass therefore a greater inertia

Newtonrsquos 2nd law of Motion- the law of acceleration

bull The unbalanced force acting on an object equals the objectrsquos mass times its acceleration

bull Force = Mass x Acceleration

Example pushing a cart

The greater the mass the more force needed to cause acceleration

Bumper cars

There are 4 rules1 If you use only one unit to start put it over a

12 Determine the conversion factors (Ex 12

inches = 1 ft) and put into a fraction3 Properly place the conversion factors in an

equation4 Check cancellations of units so that you are

left with the unit you were looking for on the top of a division bar The units that are canceled should be on opposite sides of the division bar

Example 1 How many feet in 13 in 1 112 or 1083 ftStep 1hellip starting with 13 sohellip 13 inches

1

Step 2hellip conversion factors 1 foot or 12 inches 12 inches 1 foot

Step 3hellip place factors 13 inches x 1 foot 1 12 inches

Step 4hellip check cancellations 13 inches x 1 foot 1 12

inches

13 inches = 1083 ft

Example 2 Convert 13 inches into yards

Step 1hellip starting with 13 sohellip 13 in

1

Step 2hellip conversion factors 1 ft 1 yd

12 in 3 ft

Step 3hellip place factors 13 in x 1 ft x 1 yd =

1 12 in 3 ft

Step 4hellip check cancellations 13 in x 1 ft x 1 yd

1 12 in 3 ft

13 in = 036 yd

Example 3 Convert 2 years into seconds

2 yrs x 365 days x 24 h x 60 min x 60 sec

1 1 yr 1 day 1 h 1 min

2 yrs = 63072000 sec

Example 4 Convert 4 decades into minutes

4 dec x 10 yrs x 365 days x 24 h x 60 min

1 1 dec 1 yr 1 day 1 h

4 decades = 21024000 m

Example 5 I am 5rsquo 3rdquo or (5 x 12) + 3 = 63 inches tall How many cm tall am I

63 in x 256 cm =

1 1 in

63 in = 1601 cm

Dimensional Analysis Worksheet

1 In New Jersey students in public schools go to school for 4 years How many minutes are students enrolled in high school

4 years x 365 days x 24 h x 60 min

1 1 yr 1 day 1 h

4 yrs = 2102400 min

2 Alaynarsquos dog is 3 ft tall What is the dogrsquos height in mm

3 ft x 12 in x 254 cm x 10 mm

1 1 ft 1 in 1 cm

3 ft = 9144 mm

3 Brian and Jesse were on a bus trip going 50 MPH For some extra fun they decided to convert the busrsquos speed into kmh What should their answer be

50 miles x 161 km 1 hr 1 mile

50 MPH = 805 kmh

4 Driving home from practice Alexrsquos mother was driving at a speed of 30 ms What was their speed in kmh

30 m x 1 km x 60 s x 60 min 1 s 1000 m 1 min 1 h

30 ms = 108 kmh

5 Saskia was riding her bike down the road at a speed of 5 kmh What was her speed in ms

5 km x 1000 m x 1 hr x 1 min 1 h 1 km 60 min 60 s

5 kmh = 139 ms

Class experiment

1 Determine how tall you are in inches

2 Using the conversion factor 1 mile = 161 km determine how tall you are in cm

3 Check your answer with a meter stick

AccelerationWhen you accelerate what are you doing

Speeding uphellip accelerating

When you slow down what are you doing

Decelerating

In physics we use the same term ldquoaccelerationrdquo for both speeding up and slowing down We distinguish between the two by assigning positive or negative values

+ acceleration as in speeding up positive

- acceleration as in slowing down negative

Acceleration = the change in velocity over time

- measured in ms or ms2

s

Acceleration = ∆ Velocity

∆ Time

Acceleration = ∆ Distance + Direction

∆ Time

∆ Time

Given an object moving in a circle

- ∆ velocity due to a ∆ direction

- if ∆ velocity the ∆ acceleration as well

- circular motion = ∆ D = ∆ V = ∆ A

Graphing Acceleration

A = ∆ V and slope = ∆ Y

∆ T ∆ X

Acceleration = ∆ V = ∆ Y = Slope of line

∆ T ∆ X

So Acceleration = Slope of line

Steep slope = fast movement

Gradual slope = slow movement

Acceleration Deceleration

V

T

V

T

Steepness of the line indicates the degree of acceleration

V

T

V

T

Comparing Velocity and Acceleration

Velocity = ∆ Distance Acceleration = ∆ Velocity

∆ Time ∆ Time

D

T

These two lines indicate the exact same thing the same rate of acceleration

bull Acceleration = + slope

bull Deceleration = - slope

T

V

+ slope

- slope

When object is a rest Velocity is zero

If ∆ Distance = 0 then ∆ Velocityhellip so Acceleration = 0

D

T

V

T

0

When acceleration equals zero

A= ∆ V no change in velocity

∆ T Time will always pass

No change in velocity

- no velocity ndash V = 0 then object is at rest

- constant velocity - ∆ V = Vfinal ndash Vinitial

Vf = 50 milesh and Vi = 50 milesh

Then ∆ V = 0

If acceleration = zero you are either stopped or on cruise control

To determine which you must find if there is a change in distance

How it all fits togetherFrom Motion Acceleration only one variable is

added at a time1 Motion = ∆ Distance2 Speed = ∆ Distance

∆ Time3 Velocity = ∆ Distance + Direction

∆ Time4 Acceleration = ∆ Distance + Direction

∆ Time∆ Time

Momentum

When an object is in motion we think velocity However we must not forget Momentum ndash which is also acting on the object

Momentum = a quantity defined as the product of an objectrsquos mass and its velocity - In a formula P = momentum- momentum moves in the same direction as the velocity

P = Mass x Velocity

- Measured in kgms

Momentum and ∆ Velocity

- large momentum difficult to change velocity

- small momentum easier to change velocity

Class Experiment Red light green light

Stationary objects have momentum of zero

Why No motion = no speed = no velocity = no momentum

Momentum is directly proportional to masshellip momentum increases as mass increases

P

Mass (kg)

Force

Force = the cause of acceleration or a change in velocity

- force is measured in units called Newtons

Net force = the combination of all the forces acting upon an object

bull The size of the arrow represents the amount of forcehellip

bull The arrows are the same so there is no movement

Friction

Friction = the force between two objects in contact that opposes the motion of either object

Pretend you are in a helicopter looking down on a ski slope in early springhellip The ice is meltinghellip Patches of dirt and gravel begin to showhellip

How much friction

Skis + snow = little frictionhellip skis move over snow

Skis + dirt = a lot of frictionhellip skis do not move over dirt

Air resistance is a type of friction

Gravity

Gravity = Force of attraction between 2 objects due to their masses

The force of gravity is different on different planets moons etc

On earth g = 98ms2

Gravity depends upon the masses as well as the distance between objects

Newtonrsquos Laws of Motion

Newtonrsquos 1st Law- the law of inertia

An object at rest remains at rest and an object in motion remains in motion unless it experiences an unbalanced force

bull Example 1 Whiplash ndash Person B is stopped at a traffic light Person A is not paying attention and rear-ends Person B

bull Result Person B moves forward suddenlyhellip Their head snaps back as it attempts to ldquoremain at restrdquo Their body attached to the seat moves forwardhellip their head snaps forward to catch up with the body resulting in whiplash

Example 2 Bus ride - The bus driver does not like children Every time they get too loud he slams on the breaks Why does he do this

Inertia = The tendency of an object to remain at rest or in motion with a constant velocity All objects have inertia because they resist changes in motion

Trivia If two people on a space ship (in space) get into a physical fight which will win

Person A Person B

Even though they are weightlesshellip there is no gravity Person A has a greater mass therefore a greater inertia

Newtonrsquos 2nd law of Motion- the law of acceleration

bull The unbalanced force acting on an object equals the objectrsquos mass times its acceleration

bull Force = Mass x Acceleration

Example pushing a cart

The greater the mass the more force needed to cause acceleration

Bumper cars

Example 1 How many feet in 13 in 1 112 or 1083 ftStep 1hellip starting with 13 sohellip 13 inches

1

Step 2hellip conversion factors 1 foot or 12 inches 12 inches 1 foot

Step 3hellip place factors 13 inches x 1 foot 1 12 inches

Step 4hellip check cancellations 13 inches x 1 foot 1 12

inches

13 inches = 1083 ft

Example 2 Convert 13 inches into yards

Step 1hellip starting with 13 sohellip 13 in

1

Step 2hellip conversion factors 1 ft 1 yd

12 in 3 ft

Step 3hellip place factors 13 in x 1 ft x 1 yd =

1 12 in 3 ft

Step 4hellip check cancellations 13 in x 1 ft x 1 yd

1 12 in 3 ft

13 in = 036 yd

Example 3 Convert 2 years into seconds

2 yrs x 365 days x 24 h x 60 min x 60 sec

1 1 yr 1 day 1 h 1 min

2 yrs = 63072000 sec

Example 4 Convert 4 decades into minutes

4 dec x 10 yrs x 365 days x 24 h x 60 min

1 1 dec 1 yr 1 day 1 h

4 decades = 21024000 m

Example 5 I am 5rsquo 3rdquo or (5 x 12) + 3 = 63 inches tall How many cm tall am I

63 in x 256 cm =

1 1 in

63 in = 1601 cm

Dimensional Analysis Worksheet

1 In New Jersey students in public schools go to school for 4 years How many minutes are students enrolled in high school

4 years x 365 days x 24 h x 60 min

1 1 yr 1 day 1 h

4 yrs = 2102400 min

2 Alaynarsquos dog is 3 ft tall What is the dogrsquos height in mm

3 ft x 12 in x 254 cm x 10 mm

1 1 ft 1 in 1 cm

3 ft = 9144 mm

3 Brian and Jesse were on a bus trip going 50 MPH For some extra fun they decided to convert the busrsquos speed into kmh What should their answer be

50 miles x 161 km 1 hr 1 mile

50 MPH = 805 kmh

4 Driving home from practice Alexrsquos mother was driving at a speed of 30 ms What was their speed in kmh

30 m x 1 km x 60 s x 60 min 1 s 1000 m 1 min 1 h

30 ms = 108 kmh

5 Saskia was riding her bike down the road at a speed of 5 kmh What was her speed in ms

5 km x 1000 m x 1 hr x 1 min 1 h 1 km 60 min 60 s

5 kmh = 139 ms

Class experiment

1 Determine how tall you are in inches

2 Using the conversion factor 1 mile = 161 km determine how tall you are in cm

3 Check your answer with a meter stick

AccelerationWhen you accelerate what are you doing

Speeding uphellip accelerating

When you slow down what are you doing

Decelerating

In physics we use the same term ldquoaccelerationrdquo for both speeding up and slowing down We distinguish between the two by assigning positive or negative values

+ acceleration as in speeding up positive

- acceleration as in slowing down negative

Acceleration = the change in velocity over time

- measured in ms or ms2

s

Acceleration = ∆ Velocity

∆ Time

Acceleration = ∆ Distance + Direction

∆ Time

∆ Time

Given an object moving in a circle

- ∆ velocity due to a ∆ direction

- if ∆ velocity the ∆ acceleration as well

- circular motion = ∆ D = ∆ V = ∆ A

Graphing Acceleration

A = ∆ V and slope = ∆ Y

∆ T ∆ X

Acceleration = ∆ V = ∆ Y = Slope of line

∆ T ∆ X

So Acceleration = Slope of line

Steep slope = fast movement

Gradual slope = slow movement

Acceleration Deceleration

V

T

V

T

Steepness of the line indicates the degree of acceleration

V

T

V

T

Comparing Velocity and Acceleration

Velocity = ∆ Distance Acceleration = ∆ Velocity

∆ Time ∆ Time

D

T

These two lines indicate the exact same thing the same rate of acceleration

bull Acceleration = + slope

bull Deceleration = - slope

T

V

+ slope

- slope

When object is a rest Velocity is zero

If ∆ Distance = 0 then ∆ Velocityhellip so Acceleration = 0

D

T

V

T

0

When acceleration equals zero

A= ∆ V no change in velocity

∆ T Time will always pass

No change in velocity

- no velocity ndash V = 0 then object is at rest

- constant velocity - ∆ V = Vfinal ndash Vinitial

Vf = 50 milesh and Vi = 50 milesh

Then ∆ V = 0

If acceleration = zero you are either stopped or on cruise control

To determine which you must find if there is a change in distance

How it all fits togetherFrom Motion Acceleration only one variable is

added at a time1 Motion = ∆ Distance2 Speed = ∆ Distance

∆ Time3 Velocity = ∆ Distance + Direction

∆ Time4 Acceleration = ∆ Distance + Direction

∆ Time∆ Time

Momentum

When an object is in motion we think velocity However we must not forget Momentum ndash which is also acting on the object

Momentum = a quantity defined as the product of an objectrsquos mass and its velocity - In a formula P = momentum- momentum moves in the same direction as the velocity

P = Mass x Velocity

- Measured in kgms

Momentum and ∆ Velocity

- large momentum difficult to change velocity

- small momentum easier to change velocity

Class Experiment Red light green light

Stationary objects have momentum of zero

Why No motion = no speed = no velocity = no momentum

Momentum is directly proportional to masshellip momentum increases as mass increases

P

Mass (kg)

Force

Force = the cause of acceleration or a change in velocity

- force is measured in units called Newtons

Net force = the combination of all the forces acting upon an object

bull The size of the arrow represents the amount of forcehellip

bull The arrows are the same so there is no movement

Friction

Friction = the force between two objects in contact that opposes the motion of either object

Pretend you are in a helicopter looking down on a ski slope in early springhellip The ice is meltinghellip Patches of dirt and gravel begin to showhellip

How much friction

Skis + snow = little frictionhellip skis move over snow

Skis + dirt = a lot of frictionhellip skis do not move over dirt

Air resistance is a type of friction

Gravity

Gravity = Force of attraction between 2 objects due to their masses

The force of gravity is different on different planets moons etc

On earth g = 98ms2

Gravity depends upon the masses as well as the distance between objects

Newtonrsquos Laws of Motion

Newtonrsquos 1st Law- the law of inertia

An object at rest remains at rest and an object in motion remains in motion unless it experiences an unbalanced force

bull Example 1 Whiplash ndash Person B is stopped at a traffic light Person A is not paying attention and rear-ends Person B

bull Result Person B moves forward suddenlyhellip Their head snaps back as it attempts to ldquoremain at restrdquo Their body attached to the seat moves forwardhellip their head snaps forward to catch up with the body resulting in whiplash

Example 2 Bus ride - The bus driver does not like children Every time they get too loud he slams on the breaks Why does he do this

Inertia = The tendency of an object to remain at rest or in motion with a constant velocity All objects have inertia because they resist changes in motion

Trivia If two people on a space ship (in space) get into a physical fight which will win

Person A Person B

Even though they are weightlesshellip there is no gravity Person A has a greater mass therefore a greater inertia

Newtonrsquos 2nd law of Motion- the law of acceleration

bull The unbalanced force acting on an object equals the objectrsquos mass times its acceleration

bull Force = Mass x Acceleration

Example pushing a cart

The greater the mass the more force needed to cause acceleration

Bumper cars

Example 2 Convert 13 inches into yards

Step 1hellip starting with 13 sohellip 13 in

1

Step 2hellip conversion factors 1 ft 1 yd

12 in 3 ft

Step 3hellip place factors 13 in x 1 ft x 1 yd =

1 12 in 3 ft

Step 4hellip check cancellations 13 in x 1 ft x 1 yd

1 12 in 3 ft

13 in = 036 yd

Example 3 Convert 2 years into seconds

2 yrs x 365 days x 24 h x 60 min x 60 sec

1 1 yr 1 day 1 h 1 min

2 yrs = 63072000 sec

Example 4 Convert 4 decades into minutes

4 dec x 10 yrs x 365 days x 24 h x 60 min

1 1 dec 1 yr 1 day 1 h

4 decades = 21024000 m

Example 5 I am 5rsquo 3rdquo or (5 x 12) + 3 = 63 inches tall How many cm tall am I

63 in x 256 cm =

1 1 in

63 in = 1601 cm

Dimensional Analysis Worksheet

1 In New Jersey students in public schools go to school for 4 years How many minutes are students enrolled in high school

4 years x 365 days x 24 h x 60 min

1 1 yr 1 day 1 h

4 yrs = 2102400 min

2 Alaynarsquos dog is 3 ft tall What is the dogrsquos height in mm

3 ft x 12 in x 254 cm x 10 mm

1 1 ft 1 in 1 cm

3 ft = 9144 mm

3 Brian and Jesse were on a bus trip going 50 MPH For some extra fun they decided to convert the busrsquos speed into kmh What should their answer be

50 miles x 161 km 1 hr 1 mile

50 MPH = 805 kmh

4 Driving home from practice Alexrsquos mother was driving at a speed of 30 ms What was their speed in kmh

30 m x 1 km x 60 s x 60 min 1 s 1000 m 1 min 1 h

30 ms = 108 kmh

5 Saskia was riding her bike down the road at a speed of 5 kmh What was her speed in ms

5 km x 1000 m x 1 hr x 1 min 1 h 1 km 60 min 60 s

5 kmh = 139 ms

Class experiment

1 Determine how tall you are in inches

2 Using the conversion factor 1 mile = 161 km determine how tall you are in cm

3 Check your answer with a meter stick

AccelerationWhen you accelerate what are you doing

Speeding uphellip accelerating

When you slow down what are you doing

Decelerating

In physics we use the same term ldquoaccelerationrdquo for both speeding up and slowing down We distinguish between the two by assigning positive or negative values

+ acceleration as in speeding up positive

- acceleration as in slowing down negative

Acceleration = the change in velocity over time

- measured in ms or ms2

s

Acceleration = ∆ Velocity

∆ Time

Acceleration = ∆ Distance + Direction

∆ Time

∆ Time

Given an object moving in a circle

- ∆ velocity due to a ∆ direction

- if ∆ velocity the ∆ acceleration as well

- circular motion = ∆ D = ∆ V = ∆ A

Graphing Acceleration

A = ∆ V and slope = ∆ Y

∆ T ∆ X

Acceleration = ∆ V = ∆ Y = Slope of line

∆ T ∆ X

So Acceleration = Slope of line

Steep slope = fast movement

Gradual slope = slow movement

Acceleration Deceleration

V

T

V

T

Steepness of the line indicates the degree of acceleration

V

T

V

T

Comparing Velocity and Acceleration

Velocity = ∆ Distance Acceleration = ∆ Velocity

∆ Time ∆ Time

D

T

These two lines indicate the exact same thing the same rate of acceleration

bull Acceleration = + slope

bull Deceleration = - slope

T

V

+ slope

- slope

When object is a rest Velocity is zero

If ∆ Distance = 0 then ∆ Velocityhellip so Acceleration = 0

D

T

V

T

0

When acceleration equals zero

A= ∆ V no change in velocity

∆ T Time will always pass

No change in velocity

- no velocity ndash V = 0 then object is at rest

- constant velocity - ∆ V = Vfinal ndash Vinitial

Vf = 50 milesh and Vi = 50 milesh

Then ∆ V = 0

If acceleration = zero you are either stopped or on cruise control

To determine which you must find if there is a change in distance

How it all fits togetherFrom Motion Acceleration only one variable is

added at a time1 Motion = ∆ Distance2 Speed = ∆ Distance

∆ Time3 Velocity = ∆ Distance + Direction

∆ Time4 Acceleration = ∆ Distance + Direction

∆ Time∆ Time

Momentum

When an object is in motion we think velocity However we must not forget Momentum ndash which is also acting on the object

Momentum = a quantity defined as the product of an objectrsquos mass and its velocity - In a formula P = momentum- momentum moves in the same direction as the velocity

P = Mass x Velocity

- Measured in kgms

Momentum and ∆ Velocity

- large momentum difficult to change velocity

- small momentum easier to change velocity

Class Experiment Red light green light

Stationary objects have momentum of zero

Why No motion = no speed = no velocity = no momentum

Momentum is directly proportional to masshellip momentum increases as mass increases

P

Mass (kg)

Force

Force = the cause of acceleration or a change in velocity

- force is measured in units called Newtons

Net force = the combination of all the forces acting upon an object

bull The size of the arrow represents the amount of forcehellip

bull The arrows are the same so there is no movement

Friction

Friction = the force between two objects in contact that opposes the motion of either object

Pretend you are in a helicopter looking down on a ski slope in early springhellip The ice is meltinghellip Patches of dirt and gravel begin to showhellip

How much friction

Skis + snow = little frictionhellip skis move over snow

Skis + dirt = a lot of frictionhellip skis do not move over dirt

Air resistance is a type of friction

Gravity

Gravity = Force of attraction between 2 objects due to their masses

The force of gravity is different on different planets moons etc

On earth g = 98ms2

Gravity depends upon the masses as well as the distance between objects

Newtonrsquos Laws of Motion

Newtonrsquos 1st Law- the law of inertia

An object at rest remains at rest and an object in motion remains in motion unless it experiences an unbalanced force

bull Example 1 Whiplash ndash Person B is stopped at a traffic light Person A is not paying attention and rear-ends Person B

bull Result Person B moves forward suddenlyhellip Their head snaps back as it attempts to ldquoremain at restrdquo Their body attached to the seat moves forwardhellip their head snaps forward to catch up with the body resulting in whiplash

Example 2 Bus ride - The bus driver does not like children Every time they get too loud he slams on the breaks Why does he do this

Inertia = The tendency of an object to remain at rest or in motion with a constant velocity All objects have inertia because they resist changes in motion

Trivia If two people on a space ship (in space) get into a physical fight which will win

Person A Person B

Even though they are weightlesshellip there is no gravity Person A has a greater mass therefore a greater inertia

Newtonrsquos 2nd law of Motion- the law of acceleration

bull The unbalanced force acting on an object equals the objectrsquos mass times its acceleration

bull Force = Mass x Acceleration

Example pushing a cart

The greater the mass the more force needed to cause acceleration

Bumper cars

Example 3 Convert 2 years into seconds

2 yrs x 365 days x 24 h x 60 min x 60 sec

1 1 yr 1 day 1 h 1 min

2 yrs = 63072000 sec

Example 4 Convert 4 decades into minutes

4 dec x 10 yrs x 365 days x 24 h x 60 min

1 1 dec 1 yr 1 day 1 h

4 decades = 21024000 m

Example 5 I am 5rsquo 3rdquo or (5 x 12) + 3 = 63 inches tall How many cm tall am I

63 in x 256 cm =

1 1 in

63 in = 1601 cm

Dimensional Analysis Worksheet

1 In New Jersey students in public schools go to school for 4 years How many minutes are students enrolled in high school

4 years x 365 days x 24 h x 60 min

1 1 yr 1 day 1 h

4 yrs = 2102400 min

2 Alaynarsquos dog is 3 ft tall What is the dogrsquos height in mm

3 ft x 12 in x 254 cm x 10 mm

1 1 ft 1 in 1 cm

3 ft = 9144 mm

3 Brian and Jesse were on a bus trip going 50 MPH For some extra fun they decided to convert the busrsquos speed into kmh What should their answer be

50 miles x 161 km 1 hr 1 mile

50 MPH = 805 kmh

4 Driving home from practice Alexrsquos mother was driving at a speed of 30 ms What was their speed in kmh

30 m x 1 km x 60 s x 60 min 1 s 1000 m 1 min 1 h

30 ms = 108 kmh

5 Saskia was riding her bike down the road at a speed of 5 kmh What was her speed in ms

5 km x 1000 m x 1 hr x 1 min 1 h 1 km 60 min 60 s

5 kmh = 139 ms

Class experiment

1 Determine how tall you are in inches

2 Using the conversion factor 1 mile = 161 km determine how tall you are in cm

3 Check your answer with a meter stick

AccelerationWhen you accelerate what are you doing

Speeding uphellip accelerating

When you slow down what are you doing

Decelerating

In physics we use the same term ldquoaccelerationrdquo for both speeding up and slowing down We distinguish between the two by assigning positive or negative values

+ acceleration as in speeding up positive

- acceleration as in slowing down negative

Acceleration = the change in velocity over time

- measured in ms or ms2

s

Acceleration = ∆ Velocity

∆ Time

Acceleration = ∆ Distance + Direction

∆ Time

∆ Time

Given an object moving in a circle

- ∆ velocity due to a ∆ direction

- if ∆ velocity the ∆ acceleration as well

- circular motion = ∆ D = ∆ V = ∆ A

Graphing Acceleration

A = ∆ V and slope = ∆ Y

∆ T ∆ X

Acceleration = ∆ V = ∆ Y = Slope of line

∆ T ∆ X

So Acceleration = Slope of line

Steep slope = fast movement

Gradual slope = slow movement

Acceleration Deceleration

V

T

V

T

Steepness of the line indicates the degree of acceleration

V

T

V

T

Comparing Velocity and Acceleration

Velocity = ∆ Distance Acceleration = ∆ Velocity

∆ Time ∆ Time

D

T

These two lines indicate the exact same thing the same rate of acceleration

bull Acceleration = + slope

bull Deceleration = - slope

T

V

+ slope

- slope

When object is a rest Velocity is zero

If ∆ Distance = 0 then ∆ Velocityhellip so Acceleration = 0

D

T

V

T

0

When acceleration equals zero

A= ∆ V no change in velocity

∆ T Time will always pass

No change in velocity

- no velocity ndash V = 0 then object is at rest

- constant velocity - ∆ V = Vfinal ndash Vinitial

Vf = 50 milesh and Vi = 50 milesh

Then ∆ V = 0

If acceleration = zero you are either stopped or on cruise control

To determine which you must find if there is a change in distance

How it all fits togetherFrom Motion Acceleration only one variable is

added at a time1 Motion = ∆ Distance2 Speed = ∆ Distance

∆ Time3 Velocity = ∆ Distance + Direction

∆ Time4 Acceleration = ∆ Distance + Direction

∆ Time∆ Time

Momentum

When an object is in motion we think velocity However we must not forget Momentum ndash which is also acting on the object

Momentum = a quantity defined as the product of an objectrsquos mass and its velocity - In a formula P = momentum- momentum moves in the same direction as the velocity

P = Mass x Velocity

- Measured in kgms

Momentum and ∆ Velocity

- large momentum difficult to change velocity

- small momentum easier to change velocity

Class Experiment Red light green light

Stationary objects have momentum of zero

Why No motion = no speed = no velocity = no momentum

Momentum is directly proportional to masshellip momentum increases as mass increases

P

Mass (kg)

Force

Force = the cause of acceleration or a change in velocity

- force is measured in units called Newtons

Net force = the combination of all the forces acting upon an object

bull The size of the arrow represents the amount of forcehellip

bull The arrows are the same so there is no movement

Friction

Friction = the force between two objects in contact that opposes the motion of either object

Pretend you are in a helicopter looking down on a ski slope in early springhellip The ice is meltinghellip Patches of dirt and gravel begin to showhellip

How much friction

Skis + snow = little frictionhellip skis move over snow

Skis + dirt = a lot of frictionhellip skis do not move over dirt

Air resistance is a type of friction

Gravity

Gravity = Force of attraction between 2 objects due to their masses

The force of gravity is different on different planets moons etc

On earth g = 98ms2

Gravity depends upon the masses as well as the distance between objects

Newtonrsquos Laws of Motion

Newtonrsquos 1st Law- the law of inertia

An object at rest remains at rest and an object in motion remains in motion unless it experiences an unbalanced force

bull Example 1 Whiplash ndash Person B is stopped at a traffic light Person A is not paying attention and rear-ends Person B

bull Result Person B moves forward suddenlyhellip Their head snaps back as it attempts to ldquoremain at restrdquo Their body attached to the seat moves forwardhellip their head snaps forward to catch up with the body resulting in whiplash

Example 2 Bus ride - The bus driver does not like children Every time they get too loud he slams on the breaks Why does he do this

Inertia = The tendency of an object to remain at rest or in motion with a constant velocity All objects have inertia because they resist changes in motion

Trivia If two people on a space ship (in space) get into a physical fight which will win

Person A Person B

Even though they are weightlesshellip there is no gravity Person A has a greater mass therefore a greater inertia

Newtonrsquos 2nd law of Motion- the law of acceleration

bull The unbalanced force acting on an object equals the objectrsquos mass times its acceleration

bull Force = Mass x Acceleration

Example pushing a cart

The greater the mass the more force needed to cause acceleration

Bumper cars

Example 4 Convert 4 decades into minutes

4 dec x 10 yrs x 365 days x 24 h x 60 min

1 1 dec 1 yr 1 day 1 h

4 decades = 21024000 m

Example 5 I am 5rsquo 3rdquo or (5 x 12) + 3 = 63 inches tall How many cm tall am I

63 in x 256 cm =

1 1 in

63 in = 1601 cm

Dimensional Analysis Worksheet

1 In New Jersey students in public schools go to school for 4 years How many minutes are students enrolled in high school

4 years x 365 days x 24 h x 60 min

1 1 yr 1 day 1 h

4 yrs = 2102400 min

2 Alaynarsquos dog is 3 ft tall What is the dogrsquos height in mm

3 ft x 12 in x 254 cm x 10 mm

1 1 ft 1 in 1 cm

3 ft = 9144 mm

3 Brian and Jesse were on a bus trip going 50 MPH For some extra fun they decided to convert the busrsquos speed into kmh What should their answer be

50 miles x 161 km 1 hr 1 mile

50 MPH = 805 kmh

4 Driving home from practice Alexrsquos mother was driving at a speed of 30 ms What was their speed in kmh

30 m x 1 km x 60 s x 60 min 1 s 1000 m 1 min 1 h

30 ms = 108 kmh

5 Saskia was riding her bike down the road at a speed of 5 kmh What was her speed in ms

5 km x 1000 m x 1 hr x 1 min 1 h 1 km 60 min 60 s

5 kmh = 139 ms

Class experiment

1 Determine how tall you are in inches

2 Using the conversion factor 1 mile = 161 km determine how tall you are in cm

3 Check your answer with a meter stick

AccelerationWhen you accelerate what are you doing

Speeding uphellip accelerating

When you slow down what are you doing

Decelerating

In physics we use the same term ldquoaccelerationrdquo for both speeding up and slowing down We distinguish between the two by assigning positive or negative values

+ acceleration as in speeding up positive

- acceleration as in slowing down negative

Acceleration = the change in velocity over time

- measured in ms or ms2

s

Acceleration = ∆ Velocity

∆ Time

Acceleration = ∆ Distance + Direction

∆ Time

∆ Time

Given an object moving in a circle

- ∆ velocity due to a ∆ direction

- if ∆ velocity the ∆ acceleration as well

- circular motion = ∆ D = ∆ V = ∆ A

Graphing Acceleration

A = ∆ V and slope = ∆ Y

∆ T ∆ X

Acceleration = ∆ V = ∆ Y = Slope of line

∆ T ∆ X

So Acceleration = Slope of line

Steep slope = fast movement

Gradual slope = slow movement

Acceleration Deceleration

V

T

V

T

Steepness of the line indicates the degree of acceleration

V

T

V

T

Comparing Velocity and Acceleration

Velocity = ∆ Distance Acceleration = ∆ Velocity

∆ Time ∆ Time

D

T

These two lines indicate the exact same thing the same rate of acceleration

bull Acceleration = + slope

bull Deceleration = - slope

T

V

+ slope

- slope

When object is a rest Velocity is zero

If ∆ Distance = 0 then ∆ Velocityhellip so Acceleration = 0

D

T

V

T

0

When acceleration equals zero

A= ∆ V no change in velocity

∆ T Time will always pass

No change in velocity

- no velocity ndash V = 0 then object is at rest

- constant velocity - ∆ V = Vfinal ndash Vinitial

Vf = 50 milesh and Vi = 50 milesh

Then ∆ V = 0

If acceleration = zero you are either stopped or on cruise control

To determine which you must find if there is a change in distance

How it all fits togetherFrom Motion Acceleration only one variable is

added at a time1 Motion = ∆ Distance2 Speed = ∆ Distance

∆ Time3 Velocity = ∆ Distance + Direction

∆ Time4 Acceleration = ∆ Distance + Direction

∆ Time∆ Time

Momentum

When an object is in motion we think velocity However we must not forget Momentum ndash which is also acting on the object

Momentum = a quantity defined as the product of an objectrsquos mass and its velocity - In a formula P = momentum- momentum moves in the same direction as the velocity

P = Mass x Velocity

- Measured in kgms

Momentum and ∆ Velocity

- large momentum difficult to change velocity

- small momentum easier to change velocity

Class Experiment Red light green light

Stationary objects have momentum of zero

Why No motion = no speed = no velocity = no momentum

Momentum is directly proportional to masshellip momentum increases as mass increases

P

Mass (kg)

Force

Force = the cause of acceleration or a change in velocity

- force is measured in units called Newtons

Net force = the combination of all the forces acting upon an object

bull The size of the arrow represents the amount of forcehellip

bull The arrows are the same so there is no movement

Friction

Friction = the force between two objects in contact that opposes the motion of either object

Pretend you are in a helicopter looking down on a ski slope in early springhellip The ice is meltinghellip Patches of dirt and gravel begin to showhellip

How much friction

Skis + snow = little frictionhellip skis move over snow

Skis + dirt = a lot of frictionhellip skis do not move over dirt

Air resistance is a type of friction

Gravity

Gravity = Force of attraction between 2 objects due to their masses

The force of gravity is different on different planets moons etc

On earth g = 98ms2

Gravity depends upon the masses as well as the distance between objects

Newtonrsquos Laws of Motion

Newtonrsquos 1st Law- the law of inertia

An object at rest remains at rest and an object in motion remains in motion unless it experiences an unbalanced force

bull Example 1 Whiplash ndash Person B is stopped at a traffic light Person A is not paying attention and rear-ends Person B

bull Result Person B moves forward suddenlyhellip Their head snaps back as it attempts to ldquoremain at restrdquo Their body attached to the seat moves forwardhellip their head snaps forward to catch up with the body resulting in whiplash

Example 2 Bus ride - The bus driver does not like children Every time they get too loud he slams on the breaks Why does he do this

Inertia = The tendency of an object to remain at rest or in motion with a constant velocity All objects have inertia because they resist changes in motion

Trivia If two people on a space ship (in space) get into a physical fight which will win

Person A Person B

Even though they are weightlesshellip there is no gravity Person A has a greater mass therefore a greater inertia

Newtonrsquos 2nd law of Motion- the law of acceleration

bull The unbalanced force acting on an object equals the objectrsquos mass times its acceleration

bull Force = Mass x Acceleration

Example pushing a cart

The greater the mass the more force needed to cause acceleration

Bumper cars

Example 5 I am 5rsquo 3rdquo or (5 x 12) + 3 = 63 inches tall How many cm tall am I

63 in x 256 cm =

1 1 in

63 in = 1601 cm

Dimensional Analysis Worksheet

1 In New Jersey students in public schools go to school for 4 years How many minutes are students enrolled in high school

4 years x 365 days x 24 h x 60 min

1 1 yr 1 day 1 h

4 yrs = 2102400 min

2 Alaynarsquos dog is 3 ft tall What is the dogrsquos height in mm

3 ft x 12 in x 254 cm x 10 mm

1 1 ft 1 in 1 cm

3 ft = 9144 mm

3 Brian and Jesse were on a bus trip going 50 MPH For some extra fun they decided to convert the busrsquos speed into kmh What should their answer be

50 miles x 161 km 1 hr 1 mile

50 MPH = 805 kmh

4 Driving home from practice Alexrsquos mother was driving at a speed of 30 ms What was their speed in kmh

30 m x 1 km x 60 s x 60 min 1 s 1000 m 1 min 1 h

30 ms = 108 kmh

5 Saskia was riding her bike down the road at a speed of 5 kmh What was her speed in ms

5 km x 1000 m x 1 hr x 1 min 1 h 1 km 60 min 60 s

5 kmh = 139 ms

Class experiment

1 Determine how tall you are in inches

2 Using the conversion factor 1 mile = 161 km determine how tall you are in cm

3 Check your answer with a meter stick

AccelerationWhen you accelerate what are you doing

Speeding uphellip accelerating

When you slow down what are you doing

Decelerating

In physics we use the same term ldquoaccelerationrdquo for both speeding up and slowing down We distinguish between the two by assigning positive or negative values

+ acceleration as in speeding up positive

- acceleration as in slowing down negative

Acceleration = the change in velocity over time

- measured in ms or ms2

s

Acceleration = ∆ Velocity

∆ Time

Acceleration = ∆ Distance + Direction

∆ Time

∆ Time

Given an object moving in a circle

- ∆ velocity due to a ∆ direction

- if ∆ velocity the ∆ acceleration as well

- circular motion = ∆ D = ∆ V = ∆ A

Graphing Acceleration

A = ∆ V and slope = ∆ Y

∆ T ∆ X

Acceleration = ∆ V = ∆ Y = Slope of line

∆ T ∆ X

So Acceleration = Slope of line

Steep slope = fast movement

Gradual slope = slow movement

Acceleration Deceleration

V

T

V

T

Steepness of the line indicates the degree of acceleration

V

T

V

T

Comparing Velocity and Acceleration

Velocity = ∆ Distance Acceleration = ∆ Velocity

∆ Time ∆ Time

D

T

These two lines indicate the exact same thing the same rate of acceleration

bull Acceleration = + slope

bull Deceleration = - slope

T

V

+ slope

- slope

When object is a rest Velocity is zero

If ∆ Distance = 0 then ∆ Velocityhellip so Acceleration = 0

D

T

V

T

0

When acceleration equals zero

A= ∆ V no change in velocity

∆ T Time will always pass

No change in velocity

- no velocity ndash V = 0 then object is at rest

- constant velocity - ∆ V = Vfinal ndash Vinitial

Vf = 50 milesh and Vi = 50 milesh

Then ∆ V = 0

If acceleration = zero you are either stopped or on cruise control

To determine which you must find if there is a change in distance

How it all fits togetherFrom Motion Acceleration only one variable is

added at a time1 Motion = ∆ Distance2 Speed = ∆ Distance

∆ Time3 Velocity = ∆ Distance + Direction

∆ Time4 Acceleration = ∆ Distance + Direction

∆ Time∆ Time

Momentum

When an object is in motion we think velocity However we must not forget Momentum ndash which is also acting on the object

Momentum = a quantity defined as the product of an objectrsquos mass and its velocity - In a formula P = momentum- momentum moves in the same direction as the velocity

P = Mass x Velocity

- Measured in kgms

Momentum and ∆ Velocity

- large momentum difficult to change velocity

- small momentum easier to change velocity

Class Experiment Red light green light

Stationary objects have momentum of zero

Why No motion = no speed = no velocity = no momentum

Momentum is directly proportional to masshellip momentum increases as mass increases

P

Mass (kg)

Force

Force = the cause of acceleration or a change in velocity

- force is measured in units called Newtons

Net force = the combination of all the forces acting upon an object

bull The size of the arrow represents the amount of forcehellip

bull The arrows are the same so there is no movement

Friction

Friction = the force between two objects in contact that opposes the motion of either object

Pretend you are in a helicopter looking down on a ski slope in early springhellip The ice is meltinghellip Patches of dirt and gravel begin to showhellip

How much friction

Skis + snow = little frictionhellip skis move over snow

Skis + dirt = a lot of frictionhellip skis do not move over dirt

Air resistance is a type of friction

Gravity

Gravity = Force of attraction between 2 objects due to their masses

The force of gravity is different on different planets moons etc

On earth g = 98ms2

Gravity depends upon the masses as well as the distance between objects

Newtonrsquos Laws of Motion

Newtonrsquos 1st Law- the law of inertia

An object at rest remains at rest and an object in motion remains in motion unless it experiences an unbalanced force

bull Example 1 Whiplash ndash Person B is stopped at a traffic light Person A is not paying attention and rear-ends Person B

bull Result Person B moves forward suddenlyhellip Their head snaps back as it attempts to ldquoremain at restrdquo Their body attached to the seat moves forwardhellip their head snaps forward to catch up with the body resulting in whiplash

Example 2 Bus ride - The bus driver does not like children Every time they get too loud he slams on the breaks Why does he do this

Inertia = The tendency of an object to remain at rest or in motion with a constant velocity All objects have inertia because they resist changes in motion

Trivia If two people on a space ship (in space) get into a physical fight which will win

Person A Person B

Even though they are weightlesshellip there is no gravity Person A has a greater mass therefore a greater inertia

Newtonrsquos 2nd law of Motion- the law of acceleration

bull The unbalanced force acting on an object equals the objectrsquos mass times its acceleration

bull Force = Mass x Acceleration

Example pushing a cart

The greater the mass the more force needed to cause acceleration

Bumper cars

Dimensional Analysis Worksheet

1 In New Jersey students in public schools go to school for 4 years How many minutes are students enrolled in high school

4 years x 365 days x 24 h x 60 min

1 1 yr 1 day 1 h

4 yrs = 2102400 min

2 Alaynarsquos dog is 3 ft tall What is the dogrsquos height in mm

3 ft x 12 in x 254 cm x 10 mm

1 1 ft 1 in 1 cm

3 ft = 9144 mm

3 Brian and Jesse were on a bus trip going 50 MPH For some extra fun they decided to convert the busrsquos speed into kmh What should their answer be

50 miles x 161 km 1 hr 1 mile

50 MPH = 805 kmh

4 Driving home from practice Alexrsquos mother was driving at a speed of 30 ms What was their speed in kmh

30 m x 1 km x 60 s x 60 min 1 s 1000 m 1 min 1 h

30 ms = 108 kmh

5 Saskia was riding her bike down the road at a speed of 5 kmh What was her speed in ms

5 km x 1000 m x 1 hr x 1 min 1 h 1 km 60 min 60 s

5 kmh = 139 ms

Class experiment

1 Determine how tall you are in inches

2 Using the conversion factor 1 mile = 161 km determine how tall you are in cm

3 Check your answer with a meter stick

AccelerationWhen you accelerate what are you doing

Speeding uphellip accelerating

When you slow down what are you doing

Decelerating

In physics we use the same term ldquoaccelerationrdquo for both speeding up and slowing down We distinguish between the two by assigning positive or negative values

+ acceleration as in speeding up positive

- acceleration as in slowing down negative

Acceleration = the change in velocity over time

- measured in ms or ms2

s

Acceleration = ∆ Velocity

∆ Time

Acceleration = ∆ Distance + Direction

∆ Time

∆ Time

Given an object moving in a circle

- ∆ velocity due to a ∆ direction

- if ∆ velocity the ∆ acceleration as well

- circular motion = ∆ D = ∆ V = ∆ A

Graphing Acceleration

A = ∆ V and slope = ∆ Y

∆ T ∆ X

Acceleration = ∆ V = ∆ Y = Slope of line

∆ T ∆ X

So Acceleration = Slope of line

Steep slope = fast movement

Gradual slope = slow movement

Acceleration Deceleration

V

T

V

T

Steepness of the line indicates the degree of acceleration

V

T

V

T

Comparing Velocity and Acceleration

Velocity = ∆ Distance Acceleration = ∆ Velocity

∆ Time ∆ Time

D

T

These two lines indicate the exact same thing the same rate of acceleration

bull Acceleration = + slope

bull Deceleration = - slope

T

V

+ slope

- slope

When object is a rest Velocity is zero

If ∆ Distance = 0 then ∆ Velocityhellip so Acceleration = 0

D

T

V

T

0

When acceleration equals zero

A= ∆ V no change in velocity

∆ T Time will always pass

No change in velocity

- no velocity ndash V = 0 then object is at rest

- constant velocity - ∆ V = Vfinal ndash Vinitial

Vf = 50 milesh and Vi = 50 milesh

Then ∆ V = 0

If acceleration = zero you are either stopped or on cruise control

To determine which you must find if there is a change in distance

How it all fits togetherFrom Motion Acceleration only one variable is

added at a time1 Motion = ∆ Distance2 Speed = ∆ Distance

∆ Time3 Velocity = ∆ Distance + Direction

∆ Time4 Acceleration = ∆ Distance + Direction

∆ Time∆ Time

Momentum

When an object is in motion we think velocity However we must not forget Momentum ndash which is also acting on the object

Momentum = a quantity defined as the product of an objectrsquos mass and its velocity - In a formula P = momentum- momentum moves in the same direction as the velocity

P = Mass x Velocity

- Measured in kgms

Momentum and ∆ Velocity

- large momentum difficult to change velocity

- small momentum easier to change velocity

Class Experiment Red light green light

Stationary objects have momentum of zero

Why No motion = no speed = no velocity = no momentum

Momentum is directly proportional to masshellip momentum increases as mass increases

P

Mass (kg)

Force

Force = the cause of acceleration or a change in velocity

- force is measured in units called Newtons

Net force = the combination of all the forces acting upon an object

bull The size of the arrow represents the amount of forcehellip

bull The arrows are the same so there is no movement

Friction

Friction = the force between two objects in contact that opposes the motion of either object

Pretend you are in a helicopter looking down on a ski slope in early springhellip The ice is meltinghellip Patches of dirt and gravel begin to showhellip

How much friction

Skis + snow = little frictionhellip skis move over snow

Skis + dirt = a lot of frictionhellip skis do not move over dirt

Air resistance is a type of friction

Gravity

Gravity = Force of attraction between 2 objects due to their masses

The force of gravity is different on different planets moons etc

On earth g = 98ms2

Gravity depends upon the masses as well as the distance between objects

Newtonrsquos Laws of Motion

Newtonrsquos 1st Law- the law of inertia

An object at rest remains at rest and an object in motion remains in motion unless it experiences an unbalanced force

bull Example 1 Whiplash ndash Person B is stopped at a traffic light Person A is not paying attention and rear-ends Person B

bull Result Person B moves forward suddenlyhellip Their head snaps back as it attempts to ldquoremain at restrdquo Their body attached to the seat moves forwardhellip their head snaps forward to catch up with the body resulting in whiplash

Example 2 Bus ride - The bus driver does not like children Every time they get too loud he slams on the breaks Why does he do this

Inertia = The tendency of an object to remain at rest or in motion with a constant velocity All objects have inertia because they resist changes in motion

Trivia If two people on a space ship (in space) get into a physical fight which will win

Person A Person B

Even though they are weightlesshellip there is no gravity Person A has a greater mass therefore a greater inertia

Newtonrsquos 2nd law of Motion- the law of acceleration

bull The unbalanced force acting on an object equals the objectrsquos mass times its acceleration

bull Force = Mass x Acceleration

Example pushing a cart

The greater the mass the more force needed to cause acceleration

Bumper cars

2 Alaynarsquos dog is 3 ft tall What is the dogrsquos height in mm

3 ft x 12 in x 254 cm x 10 mm

1 1 ft 1 in 1 cm

3 ft = 9144 mm

3 Brian and Jesse were on a bus trip going 50 MPH For some extra fun they decided to convert the busrsquos speed into kmh What should their answer be

50 miles x 161 km 1 hr 1 mile

50 MPH = 805 kmh

4 Driving home from practice Alexrsquos mother was driving at a speed of 30 ms What was their speed in kmh

30 m x 1 km x 60 s x 60 min 1 s 1000 m 1 min 1 h

30 ms = 108 kmh

5 Saskia was riding her bike down the road at a speed of 5 kmh What was her speed in ms

5 km x 1000 m x 1 hr x 1 min 1 h 1 km 60 min 60 s

5 kmh = 139 ms

Class experiment

1 Determine how tall you are in inches

2 Using the conversion factor 1 mile = 161 km determine how tall you are in cm

3 Check your answer with a meter stick

AccelerationWhen you accelerate what are you doing

Speeding uphellip accelerating

When you slow down what are you doing

Decelerating

In physics we use the same term ldquoaccelerationrdquo for both speeding up and slowing down We distinguish between the two by assigning positive or negative values

+ acceleration as in speeding up positive

- acceleration as in slowing down negative

Acceleration = the change in velocity over time

- measured in ms or ms2

s

Acceleration = ∆ Velocity

∆ Time

Acceleration = ∆ Distance + Direction

∆ Time

∆ Time

Given an object moving in a circle

- ∆ velocity due to a ∆ direction

- if ∆ velocity the ∆ acceleration as well

- circular motion = ∆ D = ∆ V = ∆ A

Graphing Acceleration

A = ∆ V and slope = ∆ Y

∆ T ∆ X

Acceleration = ∆ V = ∆ Y = Slope of line

∆ T ∆ X

So Acceleration = Slope of line

Steep slope = fast movement

Gradual slope = slow movement

Acceleration Deceleration

V

T

V

T

Steepness of the line indicates the degree of acceleration

V

T

V

T

Comparing Velocity and Acceleration

Velocity = ∆ Distance Acceleration = ∆ Velocity

∆ Time ∆ Time

D

T

These two lines indicate the exact same thing the same rate of acceleration

bull Acceleration = + slope

bull Deceleration = - slope

T

V

+ slope

- slope

When object is a rest Velocity is zero

If ∆ Distance = 0 then ∆ Velocityhellip so Acceleration = 0

D

T

V

T

0

When acceleration equals zero

A= ∆ V no change in velocity

∆ T Time will always pass

No change in velocity

- no velocity ndash V = 0 then object is at rest

- constant velocity - ∆ V = Vfinal ndash Vinitial

Vf = 50 milesh and Vi = 50 milesh

Then ∆ V = 0

If acceleration = zero you are either stopped or on cruise control

To determine which you must find if there is a change in distance

How it all fits togetherFrom Motion Acceleration only one variable is

added at a time1 Motion = ∆ Distance2 Speed = ∆ Distance

∆ Time3 Velocity = ∆ Distance + Direction

∆ Time4 Acceleration = ∆ Distance + Direction

∆ Time∆ Time

Momentum

When an object is in motion we think velocity However we must not forget Momentum ndash which is also acting on the object

Momentum = a quantity defined as the product of an objectrsquos mass and its velocity - In a formula P = momentum- momentum moves in the same direction as the velocity

P = Mass x Velocity

- Measured in kgms

Momentum and ∆ Velocity

- large momentum difficult to change velocity

- small momentum easier to change velocity

Class Experiment Red light green light

Stationary objects have momentum of zero

Why No motion = no speed = no velocity = no momentum

Momentum is directly proportional to masshellip momentum increases as mass increases

P

Mass (kg)

Force

Force = the cause of acceleration or a change in velocity

- force is measured in units called Newtons

Net force = the combination of all the forces acting upon an object

bull The size of the arrow represents the amount of forcehellip

bull The arrows are the same so there is no movement

Friction

Friction = the force between two objects in contact that opposes the motion of either object

Pretend you are in a helicopter looking down on a ski slope in early springhellip The ice is meltinghellip Patches of dirt and gravel begin to showhellip

How much friction

Skis + snow = little frictionhellip skis move over snow

Skis + dirt = a lot of frictionhellip skis do not move over dirt

Air resistance is a type of friction

Gravity

Gravity = Force of attraction between 2 objects due to their masses

The force of gravity is different on different planets moons etc

On earth g = 98ms2

Gravity depends upon the masses as well as the distance between objects

Newtonrsquos Laws of Motion

Newtonrsquos 1st Law- the law of inertia

An object at rest remains at rest and an object in motion remains in motion unless it experiences an unbalanced force

bull Example 1 Whiplash ndash Person B is stopped at a traffic light Person A is not paying attention and rear-ends Person B

bull Result Person B moves forward suddenlyhellip Their head snaps back as it attempts to ldquoremain at restrdquo Their body attached to the seat moves forwardhellip their head snaps forward to catch up with the body resulting in whiplash

Example 2 Bus ride - The bus driver does not like children Every time they get too loud he slams on the breaks Why does he do this

Inertia = The tendency of an object to remain at rest or in motion with a constant velocity All objects have inertia because they resist changes in motion

Trivia If two people on a space ship (in space) get into a physical fight which will win

Person A Person B

Even though they are weightlesshellip there is no gravity Person A has a greater mass therefore a greater inertia

Newtonrsquos 2nd law of Motion- the law of acceleration

bull The unbalanced force acting on an object equals the objectrsquos mass times its acceleration

bull Force = Mass x Acceleration

Example pushing a cart

The greater the mass the more force needed to cause acceleration

Bumper cars

3 Brian and Jesse were on a bus trip going 50 MPH For some extra fun they decided to convert the busrsquos speed into kmh What should their answer be

50 miles x 161 km 1 hr 1 mile

50 MPH = 805 kmh

4 Driving home from practice Alexrsquos mother was driving at a speed of 30 ms What was their speed in kmh

30 m x 1 km x 60 s x 60 min 1 s 1000 m 1 min 1 h

30 ms = 108 kmh

5 Saskia was riding her bike down the road at a speed of 5 kmh What was her speed in ms

5 km x 1000 m x 1 hr x 1 min 1 h 1 km 60 min 60 s

5 kmh = 139 ms

Class experiment

1 Determine how tall you are in inches

2 Using the conversion factor 1 mile = 161 km determine how tall you are in cm

3 Check your answer with a meter stick

AccelerationWhen you accelerate what are you doing

Speeding uphellip accelerating

When you slow down what are you doing

Decelerating

In physics we use the same term ldquoaccelerationrdquo for both speeding up and slowing down We distinguish between the two by assigning positive or negative values

+ acceleration as in speeding up positive

- acceleration as in slowing down negative

Acceleration = the change in velocity over time

- measured in ms or ms2

s

Acceleration = ∆ Velocity

∆ Time

Acceleration = ∆ Distance + Direction

∆ Time

∆ Time

Given an object moving in a circle

- ∆ velocity due to a ∆ direction

- if ∆ velocity the ∆ acceleration as well

- circular motion = ∆ D = ∆ V = ∆ A

Graphing Acceleration

A = ∆ V and slope = ∆ Y

∆ T ∆ X

Acceleration = ∆ V = ∆ Y = Slope of line

∆ T ∆ X

So Acceleration = Slope of line

Steep slope = fast movement

Gradual slope = slow movement

Acceleration Deceleration

V

T

V

T

Steepness of the line indicates the degree of acceleration

V

T

V

T

Comparing Velocity and Acceleration

Velocity = ∆ Distance Acceleration = ∆ Velocity

∆ Time ∆ Time

D

T

These two lines indicate the exact same thing the same rate of acceleration

bull Acceleration = + slope

bull Deceleration = - slope

T

V

+ slope

- slope

When object is a rest Velocity is zero

If ∆ Distance = 0 then ∆ Velocityhellip so Acceleration = 0

D

T

V

T

0

When acceleration equals zero

A= ∆ V no change in velocity

∆ T Time will always pass

No change in velocity

- no velocity ndash V = 0 then object is at rest

- constant velocity - ∆ V = Vfinal ndash Vinitial

Vf = 50 milesh and Vi = 50 milesh

Then ∆ V = 0

If acceleration = zero you are either stopped or on cruise control

To determine which you must find if there is a change in distance

How it all fits togetherFrom Motion Acceleration only one variable is

added at a time1 Motion = ∆ Distance2 Speed = ∆ Distance

∆ Time3 Velocity = ∆ Distance + Direction

∆ Time4 Acceleration = ∆ Distance + Direction

∆ Time∆ Time

Momentum

When an object is in motion we think velocity However we must not forget Momentum ndash which is also acting on the object

Momentum = a quantity defined as the product of an objectrsquos mass and its velocity - In a formula P = momentum- momentum moves in the same direction as the velocity

P = Mass x Velocity

- Measured in kgms

Momentum and ∆ Velocity

- large momentum difficult to change velocity

- small momentum easier to change velocity

Class Experiment Red light green light

Stationary objects have momentum of zero

Why No motion = no speed = no velocity = no momentum

Momentum is directly proportional to masshellip momentum increases as mass increases

P

Mass (kg)

Force

Force = the cause of acceleration or a change in velocity

- force is measured in units called Newtons

Net force = the combination of all the forces acting upon an object

bull The size of the arrow represents the amount of forcehellip

bull The arrows are the same so there is no movement

Friction

Friction = the force between two objects in contact that opposes the motion of either object

Pretend you are in a helicopter looking down on a ski slope in early springhellip The ice is meltinghellip Patches of dirt and gravel begin to showhellip

How much friction

Skis + snow = little frictionhellip skis move over snow

Skis + dirt = a lot of frictionhellip skis do not move over dirt

Air resistance is a type of friction

Gravity

Gravity = Force of attraction between 2 objects due to their masses

The force of gravity is different on different planets moons etc

On earth g = 98ms2

Gravity depends upon the masses as well as the distance between objects

Newtonrsquos Laws of Motion

Newtonrsquos 1st Law- the law of inertia

An object at rest remains at rest and an object in motion remains in motion unless it experiences an unbalanced force

bull Example 1 Whiplash ndash Person B is stopped at a traffic light Person A is not paying attention and rear-ends Person B

bull Result Person B moves forward suddenlyhellip Their head snaps back as it attempts to ldquoremain at restrdquo Their body attached to the seat moves forwardhellip their head snaps forward to catch up with the body resulting in whiplash

Example 2 Bus ride - The bus driver does not like children Every time they get too loud he slams on the breaks Why does he do this

Inertia = The tendency of an object to remain at rest or in motion with a constant velocity All objects have inertia because they resist changes in motion

Trivia If two people on a space ship (in space) get into a physical fight which will win

Person A Person B

Even though they are weightlesshellip there is no gravity Person A has a greater mass therefore a greater inertia

Newtonrsquos 2nd law of Motion- the law of acceleration

bull The unbalanced force acting on an object equals the objectrsquos mass times its acceleration

bull Force = Mass x Acceleration

Example pushing a cart

The greater the mass the more force needed to cause acceleration

Bumper cars

4 Driving home from practice Alexrsquos mother was driving at a speed of 30 ms What was their speed in kmh

30 m x 1 km x 60 s x 60 min 1 s 1000 m 1 min 1 h

30 ms = 108 kmh

5 Saskia was riding her bike down the road at a speed of 5 kmh What was her speed in ms

5 km x 1000 m x 1 hr x 1 min 1 h 1 km 60 min 60 s

5 kmh = 139 ms

Class experiment

1 Determine how tall you are in inches

2 Using the conversion factor 1 mile = 161 km determine how tall you are in cm

3 Check your answer with a meter stick

AccelerationWhen you accelerate what are you doing

Speeding uphellip accelerating

When you slow down what are you doing

Decelerating

In physics we use the same term ldquoaccelerationrdquo for both speeding up and slowing down We distinguish between the two by assigning positive or negative values

+ acceleration as in speeding up positive

- acceleration as in slowing down negative

Acceleration = the change in velocity over time

- measured in ms or ms2

s

Acceleration = ∆ Velocity

∆ Time

Acceleration = ∆ Distance + Direction

∆ Time

∆ Time

Given an object moving in a circle

- ∆ velocity due to a ∆ direction

- if ∆ velocity the ∆ acceleration as well

- circular motion = ∆ D = ∆ V = ∆ A

Graphing Acceleration

A = ∆ V and slope = ∆ Y

∆ T ∆ X

Acceleration = ∆ V = ∆ Y = Slope of line

∆ T ∆ X

So Acceleration = Slope of line

Steep slope = fast movement

Gradual slope = slow movement

Acceleration Deceleration

V

T

V

T

Steepness of the line indicates the degree of acceleration

V

T

V

T

Comparing Velocity and Acceleration

Velocity = ∆ Distance Acceleration = ∆ Velocity

∆ Time ∆ Time

D

T

These two lines indicate the exact same thing the same rate of acceleration

bull Acceleration = + slope

bull Deceleration = - slope

T

V

+ slope

- slope

When object is a rest Velocity is zero

If ∆ Distance = 0 then ∆ Velocityhellip so Acceleration = 0

D

T

V

T

0

When acceleration equals zero

A= ∆ V no change in velocity

∆ T Time will always pass

No change in velocity

- no velocity ndash V = 0 then object is at rest

- constant velocity - ∆ V = Vfinal ndash Vinitial

Vf = 50 milesh and Vi = 50 milesh

Then ∆ V = 0

If acceleration = zero you are either stopped or on cruise control

To determine which you must find if there is a change in distance

How it all fits togetherFrom Motion Acceleration only one variable is

added at a time1 Motion = ∆ Distance2 Speed = ∆ Distance

∆ Time3 Velocity = ∆ Distance + Direction

∆ Time4 Acceleration = ∆ Distance + Direction

∆ Time∆ Time

Momentum

When an object is in motion we think velocity However we must not forget Momentum ndash which is also acting on the object

Momentum = a quantity defined as the product of an objectrsquos mass and its velocity - In a formula P = momentum- momentum moves in the same direction as the velocity

P = Mass x Velocity

- Measured in kgms

Momentum and ∆ Velocity

- large momentum difficult to change velocity

- small momentum easier to change velocity

Class Experiment Red light green light

Stationary objects have momentum of zero

Why No motion = no speed = no velocity = no momentum

Momentum is directly proportional to masshellip momentum increases as mass increases

P

Mass (kg)

Force

Force = the cause of acceleration or a change in velocity

- force is measured in units called Newtons

Net force = the combination of all the forces acting upon an object

bull The size of the arrow represents the amount of forcehellip

bull The arrows are the same so there is no movement

Friction

Friction = the force between two objects in contact that opposes the motion of either object

Pretend you are in a helicopter looking down on a ski slope in early springhellip The ice is meltinghellip Patches of dirt and gravel begin to showhellip

How much friction

Skis + snow = little frictionhellip skis move over snow

Skis + dirt = a lot of frictionhellip skis do not move over dirt

Air resistance is a type of friction

Gravity

Gravity = Force of attraction between 2 objects due to their masses

The force of gravity is different on different planets moons etc

On earth g = 98ms2

Gravity depends upon the masses as well as the distance between objects

Newtonrsquos Laws of Motion

Newtonrsquos 1st Law- the law of inertia

An object at rest remains at rest and an object in motion remains in motion unless it experiences an unbalanced force

bull Example 1 Whiplash ndash Person B is stopped at a traffic light Person A is not paying attention and rear-ends Person B

bull Result Person B moves forward suddenlyhellip Their head snaps back as it attempts to ldquoremain at restrdquo Their body attached to the seat moves forwardhellip their head snaps forward to catch up with the body resulting in whiplash

Example 2 Bus ride - The bus driver does not like children Every time they get too loud he slams on the breaks Why does he do this

Inertia = The tendency of an object to remain at rest or in motion with a constant velocity All objects have inertia because they resist changes in motion

Trivia If two people on a space ship (in space) get into a physical fight which will win

Person A Person B

Even though they are weightlesshellip there is no gravity Person A has a greater mass therefore a greater inertia

Newtonrsquos 2nd law of Motion- the law of acceleration

bull The unbalanced force acting on an object equals the objectrsquos mass times its acceleration

bull Force = Mass x Acceleration

Example pushing a cart

The greater the mass the more force needed to cause acceleration

Bumper cars

5 Saskia was riding her bike down the road at a speed of 5 kmh What was her speed in ms

5 km x 1000 m x 1 hr x 1 min 1 h 1 km 60 min 60 s

5 kmh = 139 ms

Class experiment

1 Determine how tall you are in inches

2 Using the conversion factor 1 mile = 161 km determine how tall you are in cm

3 Check your answer with a meter stick

AccelerationWhen you accelerate what are you doing

Speeding uphellip accelerating

When you slow down what are you doing

Decelerating

In physics we use the same term ldquoaccelerationrdquo for both speeding up and slowing down We distinguish between the two by assigning positive or negative values

+ acceleration as in speeding up positive

- acceleration as in slowing down negative

Acceleration = the change in velocity over time

- measured in ms or ms2

s

Acceleration = ∆ Velocity

∆ Time

Acceleration = ∆ Distance + Direction

∆ Time

∆ Time

Given an object moving in a circle

- ∆ velocity due to a ∆ direction

- if ∆ velocity the ∆ acceleration as well

- circular motion = ∆ D = ∆ V = ∆ A

Graphing Acceleration

A = ∆ V and slope = ∆ Y

∆ T ∆ X

Acceleration = ∆ V = ∆ Y = Slope of line

∆ T ∆ X

So Acceleration = Slope of line

Steep slope = fast movement

Gradual slope = slow movement

Acceleration Deceleration

V

T

V

T

Steepness of the line indicates the degree of acceleration

V

T

V

T

Comparing Velocity and Acceleration

Velocity = ∆ Distance Acceleration = ∆ Velocity

∆ Time ∆ Time

D

T

These two lines indicate the exact same thing the same rate of acceleration

bull Acceleration = + slope

bull Deceleration = - slope

T

V

+ slope

- slope

When object is a rest Velocity is zero

If ∆ Distance = 0 then ∆ Velocityhellip so Acceleration = 0

D

T

V

T

0

When acceleration equals zero

A= ∆ V no change in velocity

∆ T Time will always pass

No change in velocity

- no velocity ndash V = 0 then object is at rest

- constant velocity - ∆ V = Vfinal ndash Vinitial

Vf = 50 milesh and Vi = 50 milesh

Then ∆ V = 0

If acceleration = zero you are either stopped or on cruise control

To determine which you must find if there is a change in distance

How it all fits togetherFrom Motion Acceleration only one variable is

added at a time1 Motion = ∆ Distance2 Speed = ∆ Distance

∆ Time3 Velocity = ∆ Distance + Direction

∆ Time4 Acceleration = ∆ Distance + Direction

∆ Time∆ Time

Momentum

When an object is in motion we think velocity However we must not forget Momentum ndash which is also acting on the object

Momentum = a quantity defined as the product of an objectrsquos mass and its velocity - In a formula P = momentum- momentum moves in the same direction as the velocity

P = Mass x Velocity

- Measured in kgms

Momentum and ∆ Velocity

- large momentum difficult to change velocity

- small momentum easier to change velocity

Class Experiment Red light green light

Stationary objects have momentum of zero

Why No motion = no speed = no velocity = no momentum

Momentum is directly proportional to masshellip momentum increases as mass increases

P

Mass (kg)

Force

Force = the cause of acceleration or a change in velocity

- force is measured in units called Newtons

Net force = the combination of all the forces acting upon an object

bull The size of the arrow represents the amount of forcehellip

bull The arrows are the same so there is no movement

Friction

Friction = the force between two objects in contact that opposes the motion of either object

Pretend you are in a helicopter looking down on a ski slope in early springhellip The ice is meltinghellip Patches of dirt and gravel begin to showhellip

How much friction

Skis + snow = little frictionhellip skis move over snow

Skis + dirt = a lot of frictionhellip skis do not move over dirt

Air resistance is a type of friction

Gravity

Gravity = Force of attraction between 2 objects due to their masses

The force of gravity is different on different planets moons etc

On earth g = 98ms2

Gravity depends upon the masses as well as the distance between objects

Newtonrsquos Laws of Motion

Newtonrsquos 1st Law- the law of inertia

An object at rest remains at rest and an object in motion remains in motion unless it experiences an unbalanced force

bull Example 1 Whiplash ndash Person B is stopped at a traffic light Person A is not paying attention and rear-ends Person B

bull Result Person B moves forward suddenlyhellip Their head snaps back as it attempts to ldquoremain at restrdquo Their body attached to the seat moves forwardhellip their head snaps forward to catch up with the body resulting in whiplash

Example 2 Bus ride - The bus driver does not like children Every time they get too loud he slams on the breaks Why does he do this

Inertia = The tendency of an object to remain at rest or in motion with a constant velocity All objects have inertia because they resist changes in motion

Trivia If two people on a space ship (in space) get into a physical fight which will win

Person A Person B

Even though they are weightlesshellip there is no gravity Person A has a greater mass therefore a greater inertia

Newtonrsquos 2nd law of Motion- the law of acceleration

bull The unbalanced force acting on an object equals the objectrsquos mass times its acceleration

bull Force = Mass x Acceleration

Example pushing a cart

The greater the mass the more force needed to cause acceleration

Bumper cars

Class experiment

1 Determine how tall you are in inches

2 Using the conversion factor 1 mile = 161 km determine how tall you are in cm

3 Check your answer with a meter stick

AccelerationWhen you accelerate what are you doing

Speeding uphellip accelerating

When you slow down what are you doing

Decelerating

In physics we use the same term ldquoaccelerationrdquo for both speeding up and slowing down We distinguish between the two by assigning positive or negative values

+ acceleration as in speeding up positive

- acceleration as in slowing down negative

Acceleration = the change in velocity over time

- measured in ms or ms2

s

Acceleration = ∆ Velocity

∆ Time

Acceleration = ∆ Distance + Direction

∆ Time

∆ Time

Given an object moving in a circle

- ∆ velocity due to a ∆ direction

- if ∆ velocity the ∆ acceleration as well

- circular motion = ∆ D = ∆ V = ∆ A

Graphing Acceleration

A = ∆ V and slope = ∆ Y

∆ T ∆ X

Acceleration = ∆ V = ∆ Y = Slope of line

∆ T ∆ X

So Acceleration = Slope of line

Steep slope = fast movement

Gradual slope = slow movement

Acceleration Deceleration

V

T

V

T

Steepness of the line indicates the degree of acceleration

V

T

V

T

Comparing Velocity and Acceleration

Velocity = ∆ Distance Acceleration = ∆ Velocity

∆ Time ∆ Time

D

T

These two lines indicate the exact same thing the same rate of acceleration

bull Acceleration = + slope

bull Deceleration = - slope

T

V

+ slope

- slope

When object is a rest Velocity is zero

If ∆ Distance = 0 then ∆ Velocityhellip so Acceleration = 0

D

T

V

T

0

When acceleration equals zero

A= ∆ V no change in velocity

∆ T Time will always pass

No change in velocity

- no velocity ndash V = 0 then object is at rest

- constant velocity - ∆ V = Vfinal ndash Vinitial

Vf = 50 milesh and Vi = 50 milesh

Then ∆ V = 0

If acceleration = zero you are either stopped or on cruise control

To determine which you must find if there is a change in distance

How it all fits togetherFrom Motion Acceleration only one variable is

added at a time1 Motion = ∆ Distance2 Speed = ∆ Distance

∆ Time3 Velocity = ∆ Distance + Direction

∆ Time4 Acceleration = ∆ Distance + Direction

∆ Time∆ Time

Momentum

When an object is in motion we think velocity However we must not forget Momentum ndash which is also acting on the object

Momentum = a quantity defined as the product of an objectrsquos mass and its velocity - In a formula P = momentum- momentum moves in the same direction as the velocity

P = Mass x Velocity

- Measured in kgms

Momentum and ∆ Velocity

- large momentum difficult to change velocity

- small momentum easier to change velocity

Class Experiment Red light green light

Stationary objects have momentum of zero

Why No motion = no speed = no velocity = no momentum

Momentum is directly proportional to masshellip momentum increases as mass increases

P

Mass (kg)

Force

Force = the cause of acceleration or a change in velocity

- force is measured in units called Newtons

Net force = the combination of all the forces acting upon an object

bull The size of the arrow represents the amount of forcehellip

bull The arrows are the same so there is no movement

Friction

Friction = the force between two objects in contact that opposes the motion of either object

Pretend you are in a helicopter looking down on a ski slope in early springhellip The ice is meltinghellip Patches of dirt and gravel begin to showhellip

How much friction

Skis + snow = little frictionhellip skis move over snow

Skis + dirt = a lot of frictionhellip skis do not move over dirt

Air resistance is a type of friction

Gravity

Gravity = Force of attraction between 2 objects due to their masses

The force of gravity is different on different planets moons etc

On earth g = 98ms2

Gravity depends upon the masses as well as the distance between objects

Newtonrsquos Laws of Motion

Newtonrsquos 1st Law- the law of inertia

An object at rest remains at rest and an object in motion remains in motion unless it experiences an unbalanced force

bull Example 1 Whiplash ndash Person B is stopped at a traffic light Person A is not paying attention and rear-ends Person B

bull Result Person B moves forward suddenlyhellip Their head snaps back as it attempts to ldquoremain at restrdquo Their body attached to the seat moves forwardhellip their head snaps forward to catch up with the body resulting in whiplash

Example 2 Bus ride - The bus driver does not like children Every time they get too loud he slams on the breaks Why does he do this

Inertia = The tendency of an object to remain at rest or in motion with a constant velocity All objects have inertia because they resist changes in motion

Trivia If two people on a space ship (in space) get into a physical fight which will win

Person A Person B

Even though they are weightlesshellip there is no gravity Person A has a greater mass therefore a greater inertia

Newtonrsquos 2nd law of Motion- the law of acceleration

bull The unbalanced force acting on an object equals the objectrsquos mass times its acceleration

bull Force = Mass x Acceleration

Example pushing a cart

The greater the mass the more force needed to cause acceleration

Bumper cars

AccelerationWhen you accelerate what are you doing

Speeding uphellip accelerating

When you slow down what are you doing

Decelerating

In physics we use the same term ldquoaccelerationrdquo for both speeding up and slowing down We distinguish between the two by assigning positive or negative values

+ acceleration as in speeding up positive

- acceleration as in slowing down negative

Acceleration = the change in velocity over time

- measured in ms or ms2

s

Acceleration = ∆ Velocity

∆ Time

Acceleration = ∆ Distance + Direction

∆ Time

∆ Time

Given an object moving in a circle

- ∆ velocity due to a ∆ direction

- if ∆ velocity the ∆ acceleration as well

- circular motion = ∆ D = ∆ V = ∆ A

Graphing Acceleration

A = ∆ V and slope = ∆ Y

∆ T ∆ X

Acceleration = ∆ V = ∆ Y = Slope of line

∆ T ∆ X

So Acceleration = Slope of line

Steep slope = fast movement

Gradual slope = slow movement

Acceleration Deceleration

V

T

V

T

Steepness of the line indicates the degree of acceleration

V

T

V

T

Comparing Velocity and Acceleration

Velocity = ∆ Distance Acceleration = ∆ Velocity

∆ Time ∆ Time

D

T

These two lines indicate the exact same thing the same rate of acceleration

bull Acceleration = + slope

bull Deceleration = - slope

T

V

+ slope

- slope

When object is a rest Velocity is zero

If ∆ Distance = 0 then ∆ Velocityhellip so Acceleration = 0

D

T

V

T

0

When acceleration equals zero

A= ∆ V no change in velocity

∆ T Time will always pass

No change in velocity

- no velocity ndash V = 0 then object is at rest

- constant velocity - ∆ V = Vfinal ndash Vinitial

Vf = 50 milesh and Vi = 50 milesh

Then ∆ V = 0

If acceleration = zero you are either stopped or on cruise control

To determine which you must find if there is a change in distance

How it all fits togetherFrom Motion Acceleration only one variable is

added at a time1 Motion = ∆ Distance2 Speed = ∆ Distance

∆ Time3 Velocity = ∆ Distance + Direction

∆ Time4 Acceleration = ∆ Distance + Direction

∆ Time∆ Time

Momentum

When an object is in motion we think velocity However we must not forget Momentum ndash which is also acting on the object

Momentum = a quantity defined as the product of an objectrsquos mass and its velocity - In a formula P = momentum- momentum moves in the same direction as the velocity

P = Mass x Velocity

- Measured in kgms

Momentum and ∆ Velocity

- large momentum difficult to change velocity

- small momentum easier to change velocity

Class Experiment Red light green light

Stationary objects have momentum of zero

Why No motion = no speed = no velocity = no momentum

Momentum is directly proportional to masshellip momentum increases as mass increases

P

Mass (kg)

Force

Force = the cause of acceleration or a change in velocity

- force is measured in units called Newtons

Net force = the combination of all the forces acting upon an object

bull The size of the arrow represents the amount of forcehellip

bull The arrows are the same so there is no movement

Friction

Friction = the force between two objects in contact that opposes the motion of either object

Pretend you are in a helicopter looking down on a ski slope in early springhellip The ice is meltinghellip Patches of dirt and gravel begin to showhellip

How much friction

Skis + snow = little frictionhellip skis move over snow

Skis + dirt = a lot of frictionhellip skis do not move over dirt

Air resistance is a type of friction

Gravity

Gravity = Force of attraction between 2 objects due to their masses

The force of gravity is different on different planets moons etc

On earth g = 98ms2

Gravity depends upon the masses as well as the distance between objects

Newtonrsquos Laws of Motion

Newtonrsquos 1st Law- the law of inertia

An object at rest remains at rest and an object in motion remains in motion unless it experiences an unbalanced force

bull Example 1 Whiplash ndash Person B is stopped at a traffic light Person A is not paying attention and rear-ends Person B

bull Result Person B moves forward suddenlyhellip Their head snaps back as it attempts to ldquoremain at restrdquo Their body attached to the seat moves forwardhellip their head snaps forward to catch up with the body resulting in whiplash

Example 2 Bus ride - The bus driver does not like children Every time they get too loud he slams on the breaks Why does he do this

Inertia = The tendency of an object to remain at rest or in motion with a constant velocity All objects have inertia because they resist changes in motion

Trivia If two people on a space ship (in space) get into a physical fight which will win

Person A Person B

Even though they are weightlesshellip there is no gravity Person A has a greater mass therefore a greater inertia

Newtonrsquos 2nd law of Motion- the law of acceleration

bull The unbalanced force acting on an object equals the objectrsquos mass times its acceleration

bull Force = Mass x Acceleration

Example pushing a cart

The greater the mass the more force needed to cause acceleration

Bumper cars

Acceleration = the change in velocity over time

- measured in ms or ms2

s

Acceleration = ∆ Velocity

∆ Time

Acceleration = ∆ Distance + Direction

∆ Time

∆ Time

Given an object moving in a circle

- ∆ velocity due to a ∆ direction

- if ∆ velocity the ∆ acceleration as well

- circular motion = ∆ D = ∆ V = ∆ A

Graphing Acceleration

A = ∆ V and slope = ∆ Y

∆ T ∆ X

Acceleration = ∆ V = ∆ Y = Slope of line

∆ T ∆ X

So Acceleration = Slope of line

Steep slope = fast movement

Gradual slope = slow movement

Acceleration Deceleration

V

T

V

T

Steepness of the line indicates the degree of acceleration

V

T

V

T

Comparing Velocity and Acceleration

Velocity = ∆ Distance Acceleration = ∆ Velocity

∆ Time ∆ Time

D

T

These two lines indicate the exact same thing the same rate of acceleration

bull Acceleration = + slope

bull Deceleration = - slope

T

V

+ slope

- slope

When object is a rest Velocity is zero

If ∆ Distance = 0 then ∆ Velocityhellip so Acceleration = 0

D

T

V

T

0

When acceleration equals zero

A= ∆ V no change in velocity

∆ T Time will always pass

No change in velocity

- no velocity ndash V = 0 then object is at rest

- constant velocity - ∆ V = Vfinal ndash Vinitial

Vf = 50 milesh and Vi = 50 milesh

Then ∆ V = 0

If acceleration = zero you are either stopped or on cruise control

To determine which you must find if there is a change in distance

How it all fits togetherFrom Motion Acceleration only one variable is

added at a time1 Motion = ∆ Distance2 Speed = ∆ Distance

∆ Time3 Velocity = ∆ Distance + Direction

∆ Time4 Acceleration = ∆ Distance + Direction

∆ Time∆ Time

Momentum

When an object is in motion we think velocity However we must not forget Momentum ndash which is also acting on the object

Momentum = a quantity defined as the product of an objectrsquos mass and its velocity - In a formula P = momentum- momentum moves in the same direction as the velocity

P = Mass x Velocity

- Measured in kgms

Momentum and ∆ Velocity

- large momentum difficult to change velocity

- small momentum easier to change velocity

Class Experiment Red light green light

Stationary objects have momentum of zero

Why No motion = no speed = no velocity = no momentum

Momentum is directly proportional to masshellip momentum increases as mass increases

P

Mass (kg)

Force

Force = the cause of acceleration or a change in velocity

- force is measured in units called Newtons

Net force = the combination of all the forces acting upon an object

bull The size of the arrow represents the amount of forcehellip

bull The arrows are the same so there is no movement

Friction

Friction = the force between two objects in contact that opposes the motion of either object

Pretend you are in a helicopter looking down on a ski slope in early springhellip The ice is meltinghellip Patches of dirt and gravel begin to showhellip

How much friction

Skis + snow = little frictionhellip skis move over snow

Skis + dirt = a lot of frictionhellip skis do not move over dirt

Air resistance is a type of friction

Gravity

Gravity = Force of attraction between 2 objects due to their masses

The force of gravity is different on different planets moons etc

On earth g = 98ms2

Gravity depends upon the masses as well as the distance between objects

Newtonrsquos Laws of Motion

Newtonrsquos 1st Law- the law of inertia

An object at rest remains at rest and an object in motion remains in motion unless it experiences an unbalanced force

bull Example 1 Whiplash ndash Person B is stopped at a traffic light Person A is not paying attention and rear-ends Person B

bull Result Person B moves forward suddenlyhellip Their head snaps back as it attempts to ldquoremain at restrdquo Their body attached to the seat moves forwardhellip their head snaps forward to catch up with the body resulting in whiplash

Example 2 Bus ride - The bus driver does not like children Every time they get too loud he slams on the breaks Why does he do this

Inertia = The tendency of an object to remain at rest or in motion with a constant velocity All objects have inertia because they resist changes in motion

Trivia If two people on a space ship (in space) get into a physical fight which will win

Person A Person B

Even though they are weightlesshellip there is no gravity Person A has a greater mass therefore a greater inertia

Newtonrsquos 2nd law of Motion- the law of acceleration

bull The unbalanced force acting on an object equals the objectrsquos mass times its acceleration

bull Force = Mass x Acceleration

Example pushing a cart

The greater the mass the more force needed to cause acceleration

Bumper cars

Acceleration = ∆ Distance + Direction

∆ Time

∆ Time

Given an object moving in a circle

- ∆ velocity due to a ∆ direction

- if ∆ velocity the ∆ acceleration as well

- circular motion = ∆ D = ∆ V = ∆ A

Graphing Acceleration

A = ∆ V and slope = ∆ Y

∆ T ∆ X

Acceleration = ∆ V = ∆ Y = Slope of line

∆ T ∆ X

So Acceleration = Slope of line

Steep slope = fast movement

Gradual slope = slow movement

Acceleration Deceleration

V

T

V

T

Steepness of the line indicates the degree of acceleration

V

T

V

T

Comparing Velocity and Acceleration

Velocity = ∆ Distance Acceleration = ∆ Velocity

∆ Time ∆ Time

D

T

These two lines indicate the exact same thing the same rate of acceleration

bull Acceleration = + slope

bull Deceleration = - slope

T

V

+ slope

- slope

When object is a rest Velocity is zero

If ∆ Distance = 0 then ∆ Velocityhellip so Acceleration = 0

D

T

V

T

0

When acceleration equals zero

A= ∆ V no change in velocity

∆ T Time will always pass

No change in velocity

- no velocity ndash V = 0 then object is at rest

- constant velocity - ∆ V = Vfinal ndash Vinitial

Vf = 50 milesh and Vi = 50 milesh

Then ∆ V = 0

If acceleration = zero you are either stopped or on cruise control

To determine which you must find if there is a change in distance

How it all fits togetherFrom Motion Acceleration only one variable is

added at a time1 Motion = ∆ Distance2 Speed = ∆ Distance

∆ Time3 Velocity = ∆ Distance + Direction

∆ Time4 Acceleration = ∆ Distance + Direction

∆ Time∆ Time

Momentum

When an object is in motion we think velocity However we must not forget Momentum ndash which is also acting on the object

Momentum = a quantity defined as the product of an objectrsquos mass and its velocity - In a formula P = momentum- momentum moves in the same direction as the velocity

P = Mass x Velocity

- Measured in kgms

Momentum and ∆ Velocity

- large momentum difficult to change velocity

- small momentum easier to change velocity

Class Experiment Red light green light

Stationary objects have momentum of zero

Why No motion = no speed = no velocity = no momentum

Momentum is directly proportional to masshellip momentum increases as mass increases

P

Mass (kg)

Force

Force = the cause of acceleration or a change in velocity

- force is measured in units called Newtons

Net force = the combination of all the forces acting upon an object

bull The size of the arrow represents the amount of forcehellip

bull The arrows are the same so there is no movement

Friction

Friction = the force between two objects in contact that opposes the motion of either object

Pretend you are in a helicopter looking down on a ski slope in early springhellip The ice is meltinghellip Patches of dirt and gravel begin to showhellip

How much friction

Skis + snow = little frictionhellip skis move over snow

Skis + dirt = a lot of frictionhellip skis do not move over dirt

Air resistance is a type of friction

Gravity

Gravity = Force of attraction between 2 objects due to their masses

The force of gravity is different on different planets moons etc

On earth g = 98ms2

Gravity depends upon the masses as well as the distance between objects

Newtonrsquos Laws of Motion

Newtonrsquos 1st Law- the law of inertia

An object at rest remains at rest and an object in motion remains in motion unless it experiences an unbalanced force

bull Example 1 Whiplash ndash Person B is stopped at a traffic light Person A is not paying attention and rear-ends Person B

bull Result Person B moves forward suddenlyhellip Their head snaps back as it attempts to ldquoremain at restrdquo Their body attached to the seat moves forwardhellip their head snaps forward to catch up with the body resulting in whiplash

Example 2 Bus ride - The bus driver does not like children Every time they get too loud he slams on the breaks Why does he do this

Inertia = The tendency of an object to remain at rest or in motion with a constant velocity All objects have inertia because they resist changes in motion

Trivia If two people on a space ship (in space) get into a physical fight which will win

Person A Person B

Even though they are weightlesshellip there is no gravity Person A has a greater mass therefore a greater inertia

Newtonrsquos 2nd law of Motion- the law of acceleration

bull The unbalanced force acting on an object equals the objectrsquos mass times its acceleration

bull Force = Mass x Acceleration

Example pushing a cart

The greater the mass the more force needed to cause acceleration

Bumper cars

Graphing Acceleration

A = ∆ V and slope = ∆ Y

∆ T ∆ X

Acceleration = ∆ V = ∆ Y = Slope of line

∆ T ∆ X

So Acceleration = Slope of line

Steep slope = fast movement

Gradual slope = slow movement

Acceleration Deceleration

V

T

V

T

Steepness of the line indicates the degree of acceleration

V

T

V

T

Comparing Velocity and Acceleration

Velocity = ∆ Distance Acceleration = ∆ Velocity

∆ Time ∆ Time

D

T

These two lines indicate the exact same thing the same rate of acceleration

bull Acceleration = + slope

bull Deceleration = - slope

T

V

+ slope

- slope

When object is a rest Velocity is zero

If ∆ Distance = 0 then ∆ Velocityhellip so Acceleration = 0

D

T

V

T

0

When acceleration equals zero

A= ∆ V no change in velocity

∆ T Time will always pass

No change in velocity

- no velocity ndash V = 0 then object is at rest

- constant velocity - ∆ V = Vfinal ndash Vinitial

Vf = 50 milesh and Vi = 50 milesh

Then ∆ V = 0

If acceleration = zero you are either stopped or on cruise control

To determine which you must find if there is a change in distance

How it all fits togetherFrom Motion Acceleration only one variable is

added at a time1 Motion = ∆ Distance2 Speed = ∆ Distance

∆ Time3 Velocity = ∆ Distance + Direction

∆ Time4 Acceleration = ∆ Distance + Direction

∆ Time∆ Time

Momentum

When an object is in motion we think velocity However we must not forget Momentum ndash which is also acting on the object

Momentum = a quantity defined as the product of an objectrsquos mass and its velocity - In a formula P = momentum- momentum moves in the same direction as the velocity

P = Mass x Velocity

- Measured in kgms

Momentum and ∆ Velocity

- large momentum difficult to change velocity

- small momentum easier to change velocity

Class Experiment Red light green light

Stationary objects have momentum of zero

Why No motion = no speed = no velocity = no momentum

Momentum is directly proportional to masshellip momentum increases as mass increases

P

Mass (kg)

Force

Force = the cause of acceleration or a change in velocity

- force is measured in units called Newtons

Net force = the combination of all the forces acting upon an object

bull The size of the arrow represents the amount of forcehellip

bull The arrows are the same so there is no movement

Friction

Friction = the force between two objects in contact that opposes the motion of either object

Pretend you are in a helicopter looking down on a ski slope in early springhellip The ice is meltinghellip Patches of dirt and gravel begin to showhellip

How much friction

Skis + snow = little frictionhellip skis move over snow

Skis + dirt = a lot of frictionhellip skis do not move over dirt

Air resistance is a type of friction

Gravity

Gravity = Force of attraction between 2 objects due to their masses

The force of gravity is different on different planets moons etc

On earth g = 98ms2

Gravity depends upon the masses as well as the distance between objects

Newtonrsquos Laws of Motion

Newtonrsquos 1st Law- the law of inertia

An object at rest remains at rest and an object in motion remains in motion unless it experiences an unbalanced force

bull Example 1 Whiplash ndash Person B is stopped at a traffic light Person A is not paying attention and rear-ends Person B

bull Result Person B moves forward suddenlyhellip Their head snaps back as it attempts to ldquoremain at restrdquo Their body attached to the seat moves forwardhellip their head snaps forward to catch up with the body resulting in whiplash

Example 2 Bus ride - The bus driver does not like children Every time they get too loud he slams on the breaks Why does he do this

Inertia = The tendency of an object to remain at rest or in motion with a constant velocity All objects have inertia because they resist changes in motion

Trivia If two people on a space ship (in space) get into a physical fight which will win

Person A Person B

Even though they are weightlesshellip there is no gravity Person A has a greater mass therefore a greater inertia

Newtonrsquos 2nd law of Motion- the law of acceleration

bull The unbalanced force acting on an object equals the objectrsquos mass times its acceleration

bull Force = Mass x Acceleration

Example pushing a cart

The greater the mass the more force needed to cause acceleration

Bumper cars

Acceleration Deceleration

V

T

V

T

Steepness of the line indicates the degree of acceleration

V

T

V

T

Comparing Velocity and Acceleration

Velocity = ∆ Distance Acceleration = ∆ Velocity

∆ Time ∆ Time

D

T

These two lines indicate the exact same thing the same rate of acceleration

bull Acceleration = + slope

bull Deceleration = - slope

T

V

+ slope

- slope

When object is a rest Velocity is zero

If ∆ Distance = 0 then ∆ Velocityhellip so Acceleration = 0

D

T

V

T

0

When acceleration equals zero

A= ∆ V no change in velocity

∆ T Time will always pass

No change in velocity

- no velocity ndash V = 0 then object is at rest

- constant velocity - ∆ V = Vfinal ndash Vinitial

Vf = 50 milesh and Vi = 50 milesh

Then ∆ V = 0

If acceleration = zero you are either stopped or on cruise control

To determine which you must find if there is a change in distance

How it all fits togetherFrom Motion Acceleration only one variable is

added at a time1 Motion = ∆ Distance2 Speed = ∆ Distance

∆ Time3 Velocity = ∆ Distance + Direction

∆ Time4 Acceleration = ∆ Distance + Direction

∆ Time∆ Time

Momentum

When an object is in motion we think velocity However we must not forget Momentum ndash which is also acting on the object

Momentum = a quantity defined as the product of an objectrsquos mass and its velocity - In a formula P = momentum- momentum moves in the same direction as the velocity

P = Mass x Velocity

- Measured in kgms

Momentum and ∆ Velocity

- large momentum difficult to change velocity

- small momentum easier to change velocity

Class Experiment Red light green light

Stationary objects have momentum of zero

Why No motion = no speed = no velocity = no momentum

Momentum is directly proportional to masshellip momentum increases as mass increases

P

Mass (kg)

Force

Force = the cause of acceleration or a change in velocity

- force is measured in units called Newtons

Net force = the combination of all the forces acting upon an object

bull The size of the arrow represents the amount of forcehellip

bull The arrows are the same so there is no movement

Friction

Friction = the force between two objects in contact that opposes the motion of either object

Pretend you are in a helicopter looking down on a ski slope in early springhellip The ice is meltinghellip Patches of dirt and gravel begin to showhellip

How much friction

Skis + snow = little frictionhellip skis move over snow

Skis + dirt = a lot of frictionhellip skis do not move over dirt

Air resistance is a type of friction

Gravity

Gravity = Force of attraction between 2 objects due to their masses

The force of gravity is different on different planets moons etc

On earth g = 98ms2

Gravity depends upon the masses as well as the distance between objects

Newtonrsquos Laws of Motion

Newtonrsquos 1st Law- the law of inertia

An object at rest remains at rest and an object in motion remains in motion unless it experiences an unbalanced force

bull Example 1 Whiplash ndash Person B is stopped at a traffic light Person A is not paying attention and rear-ends Person B

bull Result Person B moves forward suddenlyhellip Their head snaps back as it attempts to ldquoremain at restrdquo Their body attached to the seat moves forwardhellip their head snaps forward to catch up with the body resulting in whiplash

Example 2 Bus ride - The bus driver does not like children Every time they get too loud he slams on the breaks Why does he do this

Inertia = The tendency of an object to remain at rest or in motion with a constant velocity All objects have inertia because they resist changes in motion

Trivia If two people on a space ship (in space) get into a physical fight which will win

Person A Person B

Even though they are weightlesshellip there is no gravity Person A has a greater mass therefore a greater inertia

Newtonrsquos 2nd law of Motion- the law of acceleration

bull The unbalanced force acting on an object equals the objectrsquos mass times its acceleration

bull Force = Mass x Acceleration

Example pushing a cart

The greater the mass the more force needed to cause acceleration

Bumper cars

Steepness of the line indicates the degree of acceleration

V

T

V

T

Comparing Velocity and Acceleration

Velocity = ∆ Distance Acceleration = ∆ Velocity

∆ Time ∆ Time

D

T

These two lines indicate the exact same thing the same rate of acceleration

bull Acceleration = + slope

bull Deceleration = - slope

T

V

+ slope

- slope

When object is a rest Velocity is zero

If ∆ Distance = 0 then ∆ Velocityhellip so Acceleration = 0

D

T

V

T

0

When acceleration equals zero

A= ∆ V no change in velocity

∆ T Time will always pass

No change in velocity

- no velocity ndash V = 0 then object is at rest

- constant velocity - ∆ V = Vfinal ndash Vinitial

Vf = 50 milesh and Vi = 50 milesh

Then ∆ V = 0

If acceleration = zero you are either stopped or on cruise control

To determine which you must find if there is a change in distance

How it all fits togetherFrom Motion Acceleration only one variable is

added at a time1 Motion = ∆ Distance2 Speed = ∆ Distance

∆ Time3 Velocity = ∆ Distance + Direction

∆ Time4 Acceleration = ∆ Distance + Direction

∆ Time∆ Time

Momentum

When an object is in motion we think velocity However we must not forget Momentum ndash which is also acting on the object

Momentum = a quantity defined as the product of an objectrsquos mass and its velocity - In a formula P = momentum- momentum moves in the same direction as the velocity

P = Mass x Velocity

- Measured in kgms

Momentum and ∆ Velocity

- large momentum difficult to change velocity

- small momentum easier to change velocity

Class Experiment Red light green light

Stationary objects have momentum of zero

Why No motion = no speed = no velocity = no momentum

Momentum is directly proportional to masshellip momentum increases as mass increases

P

Mass (kg)

Force

Force = the cause of acceleration or a change in velocity

- force is measured in units called Newtons

Net force = the combination of all the forces acting upon an object

bull The size of the arrow represents the amount of forcehellip

bull The arrows are the same so there is no movement

Friction

Friction = the force between two objects in contact that opposes the motion of either object

Pretend you are in a helicopter looking down on a ski slope in early springhellip The ice is meltinghellip Patches of dirt and gravel begin to showhellip

How much friction

Skis + snow = little frictionhellip skis move over snow

Skis + dirt = a lot of frictionhellip skis do not move over dirt

Air resistance is a type of friction

Gravity

Gravity = Force of attraction between 2 objects due to their masses

The force of gravity is different on different planets moons etc

On earth g = 98ms2

Gravity depends upon the masses as well as the distance between objects

Newtonrsquos Laws of Motion

Newtonrsquos 1st Law- the law of inertia

An object at rest remains at rest and an object in motion remains in motion unless it experiences an unbalanced force

bull Example 1 Whiplash ndash Person B is stopped at a traffic light Person A is not paying attention and rear-ends Person B

bull Result Person B moves forward suddenlyhellip Their head snaps back as it attempts to ldquoremain at restrdquo Their body attached to the seat moves forwardhellip their head snaps forward to catch up with the body resulting in whiplash

Example 2 Bus ride - The bus driver does not like children Every time they get too loud he slams on the breaks Why does he do this

Inertia = The tendency of an object to remain at rest or in motion with a constant velocity All objects have inertia because they resist changes in motion

Trivia If two people on a space ship (in space) get into a physical fight which will win

Person A Person B

Even though they are weightlesshellip there is no gravity Person A has a greater mass therefore a greater inertia

Newtonrsquos 2nd law of Motion- the law of acceleration

bull The unbalanced force acting on an object equals the objectrsquos mass times its acceleration

bull Force = Mass x Acceleration

Example pushing a cart

The greater the mass the more force needed to cause acceleration

Bumper cars

V

T

Comparing Velocity and Acceleration

Velocity = ∆ Distance Acceleration = ∆ Velocity

∆ Time ∆ Time

D

T

These two lines indicate the exact same thing the same rate of acceleration

bull Acceleration = + slope

bull Deceleration = - slope

T

V

+ slope

- slope

When object is a rest Velocity is zero

If ∆ Distance = 0 then ∆ Velocityhellip so Acceleration = 0

D

T

V

T

0

When acceleration equals zero

A= ∆ V no change in velocity

∆ T Time will always pass

No change in velocity

- no velocity ndash V = 0 then object is at rest

- constant velocity - ∆ V = Vfinal ndash Vinitial

Vf = 50 milesh and Vi = 50 milesh

Then ∆ V = 0

If acceleration = zero you are either stopped or on cruise control

To determine which you must find if there is a change in distance

How it all fits togetherFrom Motion Acceleration only one variable is

added at a time1 Motion = ∆ Distance2 Speed = ∆ Distance

∆ Time3 Velocity = ∆ Distance + Direction

∆ Time4 Acceleration = ∆ Distance + Direction

∆ Time∆ Time

Momentum

When an object is in motion we think velocity However we must not forget Momentum ndash which is also acting on the object

Momentum = a quantity defined as the product of an objectrsquos mass and its velocity - In a formula P = momentum- momentum moves in the same direction as the velocity

P = Mass x Velocity

- Measured in kgms

Momentum and ∆ Velocity

- large momentum difficult to change velocity

- small momentum easier to change velocity

Class Experiment Red light green light

Stationary objects have momentum of zero

Why No motion = no speed = no velocity = no momentum

Momentum is directly proportional to masshellip momentum increases as mass increases

P

Mass (kg)

Force

Force = the cause of acceleration or a change in velocity

- force is measured in units called Newtons

Net force = the combination of all the forces acting upon an object

bull The size of the arrow represents the amount of forcehellip

bull The arrows are the same so there is no movement

Friction

Friction = the force between two objects in contact that opposes the motion of either object

Pretend you are in a helicopter looking down on a ski slope in early springhellip The ice is meltinghellip Patches of dirt and gravel begin to showhellip

How much friction

Skis + snow = little frictionhellip skis move over snow

Skis + dirt = a lot of frictionhellip skis do not move over dirt

Air resistance is a type of friction

Gravity

Gravity = Force of attraction between 2 objects due to their masses

The force of gravity is different on different planets moons etc

On earth g = 98ms2

Gravity depends upon the masses as well as the distance between objects

Newtonrsquos Laws of Motion

Newtonrsquos 1st Law- the law of inertia

An object at rest remains at rest and an object in motion remains in motion unless it experiences an unbalanced force

bull Example 1 Whiplash ndash Person B is stopped at a traffic light Person A is not paying attention and rear-ends Person B

bull Result Person B moves forward suddenlyhellip Their head snaps back as it attempts to ldquoremain at restrdquo Their body attached to the seat moves forwardhellip their head snaps forward to catch up with the body resulting in whiplash

Example 2 Bus ride - The bus driver does not like children Every time they get too loud he slams on the breaks Why does he do this

Inertia = The tendency of an object to remain at rest or in motion with a constant velocity All objects have inertia because they resist changes in motion

Trivia If two people on a space ship (in space) get into a physical fight which will win

Person A Person B

Even though they are weightlesshellip there is no gravity Person A has a greater mass therefore a greater inertia

Newtonrsquos 2nd law of Motion- the law of acceleration

bull The unbalanced force acting on an object equals the objectrsquos mass times its acceleration

bull Force = Mass x Acceleration

Example pushing a cart

The greater the mass the more force needed to cause acceleration

Bumper cars

These two lines indicate the exact same thing the same rate of acceleration

bull Acceleration = + slope

bull Deceleration = - slope

T

V

+ slope

- slope

When object is a rest Velocity is zero

If ∆ Distance = 0 then ∆ Velocityhellip so Acceleration = 0

D

T

V

T

0

When acceleration equals zero

A= ∆ V no change in velocity

∆ T Time will always pass

No change in velocity

- no velocity ndash V = 0 then object is at rest

- constant velocity - ∆ V = Vfinal ndash Vinitial

Vf = 50 milesh and Vi = 50 milesh

Then ∆ V = 0

If acceleration = zero you are either stopped or on cruise control

To determine which you must find if there is a change in distance

How it all fits togetherFrom Motion Acceleration only one variable is

added at a time1 Motion = ∆ Distance2 Speed = ∆ Distance

∆ Time3 Velocity = ∆ Distance + Direction

∆ Time4 Acceleration = ∆ Distance + Direction

∆ Time∆ Time

Momentum

When an object is in motion we think velocity However we must not forget Momentum ndash which is also acting on the object

Momentum = a quantity defined as the product of an objectrsquos mass and its velocity - In a formula P = momentum- momentum moves in the same direction as the velocity

P = Mass x Velocity

- Measured in kgms

Momentum and ∆ Velocity

- large momentum difficult to change velocity

- small momentum easier to change velocity

Class Experiment Red light green light

Stationary objects have momentum of zero

Why No motion = no speed = no velocity = no momentum

Momentum is directly proportional to masshellip momentum increases as mass increases

P

Mass (kg)

Force

Force = the cause of acceleration or a change in velocity

- force is measured in units called Newtons

Net force = the combination of all the forces acting upon an object

bull The size of the arrow represents the amount of forcehellip

bull The arrows are the same so there is no movement

Friction

Friction = the force between two objects in contact that opposes the motion of either object

Pretend you are in a helicopter looking down on a ski slope in early springhellip The ice is meltinghellip Patches of dirt and gravel begin to showhellip

How much friction

Skis + snow = little frictionhellip skis move over snow

Skis + dirt = a lot of frictionhellip skis do not move over dirt

Air resistance is a type of friction

Gravity

Gravity = Force of attraction between 2 objects due to their masses

The force of gravity is different on different planets moons etc

On earth g = 98ms2

Gravity depends upon the masses as well as the distance between objects

Newtonrsquos Laws of Motion

Newtonrsquos 1st Law- the law of inertia

An object at rest remains at rest and an object in motion remains in motion unless it experiences an unbalanced force

bull Example 1 Whiplash ndash Person B is stopped at a traffic light Person A is not paying attention and rear-ends Person B

bull Result Person B moves forward suddenlyhellip Their head snaps back as it attempts to ldquoremain at restrdquo Their body attached to the seat moves forwardhellip their head snaps forward to catch up with the body resulting in whiplash

Example 2 Bus ride - The bus driver does not like children Every time they get too loud he slams on the breaks Why does he do this

Inertia = The tendency of an object to remain at rest or in motion with a constant velocity All objects have inertia because they resist changes in motion

Trivia If two people on a space ship (in space) get into a physical fight which will win

Person A Person B

Even though they are weightlesshellip there is no gravity Person A has a greater mass therefore a greater inertia

Newtonrsquos 2nd law of Motion- the law of acceleration

bull The unbalanced force acting on an object equals the objectrsquos mass times its acceleration

bull Force = Mass x Acceleration

Example pushing a cart

The greater the mass the more force needed to cause acceleration

Bumper cars

When object is a rest Velocity is zero

If ∆ Distance = 0 then ∆ Velocityhellip so Acceleration = 0

D

T

V

T

0

When acceleration equals zero

A= ∆ V no change in velocity

∆ T Time will always pass

No change in velocity

- no velocity ndash V = 0 then object is at rest

- constant velocity - ∆ V = Vfinal ndash Vinitial

Vf = 50 milesh and Vi = 50 milesh

Then ∆ V = 0

If acceleration = zero you are either stopped or on cruise control

To determine which you must find if there is a change in distance

How it all fits togetherFrom Motion Acceleration only one variable is

added at a time1 Motion = ∆ Distance2 Speed = ∆ Distance

∆ Time3 Velocity = ∆ Distance + Direction

∆ Time4 Acceleration = ∆ Distance + Direction

∆ Time∆ Time

Momentum

When an object is in motion we think velocity However we must not forget Momentum ndash which is also acting on the object

Momentum = a quantity defined as the product of an objectrsquos mass and its velocity - In a formula P = momentum- momentum moves in the same direction as the velocity

P = Mass x Velocity

- Measured in kgms

Momentum and ∆ Velocity

- large momentum difficult to change velocity

- small momentum easier to change velocity

Class Experiment Red light green light

Stationary objects have momentum of zero

Why No motion = no speed = no velocity = no momentum

Momentum is directly proportional to masshellip momentum increases as mass increases

P

Mass (kg)

Force

Force = the cause of acceleration or a change in velocity

- force is measured in units called Newtons

Net force = the combination of all the forces acting upon an object

bull The size of the arrow represents the amount of forcehellip

bull The arrows are the same so there is no movement

Friction

Friction = the force between two objects in contact that opposes the motion of either object

Pretend you are in a helicopter looking down on a ski slope in early springhellip The ice is meltinghellip Patches of dirt and gravel begin to showhellip

How much friction

Skis + snow = little frictionhellip skis move over snow

Skis + dirt = a lot of frictionhellip skis do not move over dirt

Air resistance is a type of friction

Gravity

Gravity = Force of attraction between 2 objects due to their masses

The force of gravity is different on different planets moons etc

On earth g = 98ms2

Gravity depends upon the masses as well as the distance between objects

Newtonrsquos Laws of Motion

Newtonrsquos 1st Law- the law of inertia

An object at rest remains at rest and an object in motion remains in motion unless it experiences an unbalanced force

bull Example 1 Whiplash ndash Person B is stopped at a traffic light Person A is not paying attention and rear-ends Person B

bull Result Person B moves forward suddenlyhellip Their head snaps back as it attempts to ldquoremain at restrdquo Their body attached to the seat moves forwardhellip their head snaps forward to catch up with the body resulting in whiplash

Example 2 Bus ride - The bus driver does not like children Every time they get too loud he slams on the breaks Why does he do this

Inertia = The tendency of an object to remain at rest or in motion with a constant velocity All objects have inertia because they resist changes in motion

Trivia If two people on a space ship (in space) get into a physical fight which will win

Person A Person B

Even though they are weightlesshellip there is no gravity Person A has a greater mass therefore a greater inertia

Newtonrsquos 2nd law of Motion- the law of acceleration

bull The unbalanced force acting on an object equals the objectrsquos mass times its acceleration

bull Force = Mass x Acceleration

Example pushing a cart

The greater the mass the more force needed to cause acceleration

Bumper cars

When acceleration equals zero

A= ∆ V no change in velocity

∆ T Time will always pass

No change in velocity

- no velocity ndash V = 0 then object is at rest

- constant velocity - ∆ V = Vfinal ndash Vinitial

Vf = 50 milesh and Vi = 50 milesh

Then ∆ V = 0

If acceleration = zero you are either stopped or on cruise control

To determine which you must find if there is a change in distance

How it all fits togetherFrom Motion Acceleration only one variable is

added at a time1 Motion = ∆ Distance2 Speed = ∆ Distance

∆ Time3 Velocity = ∆ Distance + Direction

∆ Time4 Acceleration = ∆ Distance + Direction

∆ Time∆ Time

Momentum

When an object is in motion we think velocity However we must not forget Momentum ndash which is also acting on the object

Momentum = a quantity defined as the product of an objectrsquos mass and its velocity - In a formula P = momentum- momentum moves in the same direction as the velocity

P = Mass x Velocity

- Measured in kgms

Momentum and ∆ Velocity

- large momentum difficult to change velocity

- small momentum easier to change velocity

Class Experiment Red light green light

Stationary objects have momentum of zero

Why No motion = no speed = no velocity = no momentum

Momentum is directly proportional to masshellip momentum increases as mass increases

P

Mass (kg)

Force

Force = the cause of acceleration or a change in velocity

- force is measured in units called Newtons

Net force = the combination of all the forces acting upon an object

bull The size of the arrow represents the amount of forcehellip

bull The arrows are the same so there is no movement

Friction

Friction = the force between two objects in contact that opposes the motion of either object

Pretend you are in a helicopter looking down on a ski slope in early springhellip The ice is meltinghellip Patches of dirt and gravel begin to showhellip

How much friction

Skis + snow = little frictionhellip skis move over snow

Skis + dirt = a lot of frictionhellip skis do not move over dirt

Air resistance is a type of friction

Gravity

Gravity = Force of attraction between 2 objects due to their masses

The force of gravity is different on different planets moons etc

On earth g = 98ms2

Gravity depends upon the masses as well as the distance between objects

Newtonrsquos Laws of Motion

Newtonrsquos 1st Law- the law of inertia

An object at rest remains at rest and an object in motion remains in motion unless it experiences an unbalanced force

bull Example 1 Whiplash ndash Person B is stopped at a traffic light Person A is not paying attention and rear-ends Person B

bull Result Person B moves forward suddenlyhellip Their head snaps back as it attempts to ldquoremain at restrdquo Their body attached to the seat moves forwardhellip their head snaps forward to catch up with the body resulting in whiplash

Example 2 Bus ride - The bus driver does not like children Every time they get too loud he slams on the breaks Why does he do this

Inertia = The tendency of an object to remain at rest or in motion with a constant velocity All objects have inertia because they resist changes in motion

Trivia If two people on a space ship (in space) get into a physical fight which will win

Person A Person B

Even though they are weightlesshellip there is no gravity Person A has a greater mass therefore a greater inertia

Newtonrsquos 2nd law of Motion- the law of acceleration

bull The unbalanced force acting on an object equals the objectrsquos mass times its acceleration

bull Force = Mass x Acceleration

Example pushing a cart

The greater the mass the more force needed to cause acceleration

Bumper cars

If acceleration = zero you are either stopped or on cruise control

To determine which you must find if there is a change in distance

How it all fits togetherFrom Motion Acceleration only one variable is

added at a time1 Motion = ∆ Distance2 Speed = ∆ Distance

∆ Time3 Velocity = ∆ Distance + Direction

∆ Time4 Acceleration = ∆ Distance + Direction

∆ Time∆ Time

Momentum

When an object is in motion we think velocity However we must not forget Momentum ndash which is also acting on the object

Momentum = a quantity defined as the product of an objectrsquos mass and its velocity - In a formula P = momentum- momentum moves in the same direction as the velocity

P = Mass x Velocity

- Measured in kgms

Momentum and ∆ Velocity

- large momentum difficult to change velocity

- small momentum easier to change velocity

Class Experiment Red light green light

Stationary objects have momentum of zero

Why No motion = no speed = no velocity = no momentum

Momentum is directly proportional to masshellip momentum increases as mass increases

P

Mass (kg)

Force

Force = the cause of acceleration or a change in velocity

- force is measured in units called Newtons

Net force = the combination of all the forces acting upon an object

bull The size of the arrow represents the amount of forcehellip

bull The arrows are the same so there is no movement

Friction

Friction = the force between two objects in contact that opposes the motion of either object

Pretend you are in a helicopter looking down on a ski slope in early springhellip The ice is meltinghellip Patches of dirt and gravel begin to showhellip

How much friction

Skis + snow = little frictionhellip skis move over snow

Skis + dirt = a lot of frictionhellip skis do not move over dirt

Air resistance is a type of friction

Gravity

Gravity = Force of attraction between 2 objects due to their masses

The force of gravity is different on different planets moons etc

On earth g = 98ms2

Gravity depends upon the masses as well as the distance between objects

Newtonrsquos Laws of Motion

Newtonrsquos 1st Law- the law of inertia

An object at rest remains at rest and an object in motion remains in motion unless it experiences an unbalanced force

bull Example 1 Whiplash ndash Person B is stopped at a traffic light Person A is not paying attention and rear-ends Person B

bull Result Person B moves forward suddenlyhellip Their head snaps back as it attempts to ldquoremain at restrdquo Their body attached to the seat moves forwardhellip their head snaps forward to catch up with the body resulting in whiplash

Example 2 Bus ride - The bus driver does not like children Every time they get too loud he slams on the breaks Why does he do this

Inertia = The tendency of an object to remain at rest or in motion with a constant velocity All objects have inertia because they resist changes in motion

Trivia If two people on a space ship (in space) get into a physical fight which will win

Person A Person B

Even though they are weightlesshellip there is no gravity Person A has a greater mass therefore a greater inertia

Newtonrsquos 2nd law of Motion- the law of acceleration

bull The unbalanced force acting on an object equals the objectrsquos mass times its acceleration

bull Force = Mass x Acceleration

Example pushing a cart

The greater the mass the more force needed to cause acceleration

Bumper cars

How it all fits togetherFrom Motion Acceleration only one variable is

added at a time1 Motion = ∆ Distance2 Speed = ∆ Distance

∆ Time3 Velocity = ∆ Distance + Direction

∆ Time4 Acceleration = ∆ Distance + Direction

∆ Time∆ Time

Momentum

When an object is in motion we think velocity However we must not forget Momentum ndash which is also acting on the object

Momentum = a quantity defined as the product of an objectrsquos mass and its velocity - In a formula P = momentum- momentum moves in the same direction as the velocity

P = Mass x Velocity

- Measured in kgms

Momentum and ∆ Velocity

- large momentum difficult to change velocity

- small momentum easier to change velocity

Class Experiment Red light green light

Stationary objects have momentum of zero

Why No motion = no speed = no velocity = no momentum

Momentum is directly proportional to masshellip momentum increases as mass increases

P

Mass (kg)

Force

Force = the cause of acceleration or a change in velocity

- force is measured in units called Newtons

Net force = the combination of all the forces acting upon an object

bull The size of the arrow represents the amount of forcehellip

bull The arrows are the same so there is no movement

Friction

Friction = the force between two objects in contact that opposes the motion of either object

Pretend you are in a helicopter looking down on a ski slope in early springhellip The ice is meltinghellip Patches of dirt and gravel begin to showhellip

How much friction

Skis + snow = little frictionhellip skis move over snow

Skis + dirt = a lot of frictionhellip skis do not move over dirt

Air resistance is a type of friction

Gravity

Gravity = Force of attraction between 2 objects due to their masses

The force of gravity is different on different planets moons etc

On earth g = 98ms2

Gravity depends upon the masses as well as the distance between objects

Newtonrsquos Laws of Motion

Newtonrsquos 1st Law- the law of inertia

An object at rest remains at rest and an object in motion remains in motion unless it experiences an unbalanced force

bull Example 1 Whiplash ndash Person B is stopped at a traffic light Person A is not paying attention and rear-ends Person B

bull Result Person B moves forward suddenlyhellip Their head snaps back as it attempts to ldquoremain at restrdquo Their body attached to the seat moves forwardhellip their head snaps forward to catch up with the body resulting in whiplash

Example 2 Bus ride - The bus driver does not like children Every time they get too loud he slams on the breaks Why does he do this

Inertia = The tendency of an object to remain at rest or in motion with a constant velocity All objects have inertia because they resist changes in motion

Trivia If two people on a space ship (in space) get into a physical fight which will win

Person A Person B

Even though they are weightlesshellip there is no gravity Person A has a greater mass therefore a greater inertia

Newtonrsquos 2nd law of Motion- the law of acceleration

bull The unbalanced force acting on an object equals the objectrsquos mass times its acceleration

bull Force = Mass x Acceleration

Example pushing a cart

The greater the mass the more force needed to cause acceleration

Bumper cars

Momentum

When an object is in motion we think velocity However we must not forget Momentum ndash which is also acting on the object

Momentum = a quantity defined as the product of an objectrsquos mass and its velocity - In a formula P = momentum- momentum moves in the same direction as the velocity

P = Mass x Velocity

- Measured in kgms

Momentum and ∆ Velocity

- large momentum difficult to change velocity

- small momentum easier to change velocity

Class Experiment Red light green light

Stationary objects have momentum of zero

Why No motion = no speed = no velocity = no momentum

Momentum is directly proportional to masshellip momentum increases as mass increases

P

Mass (kg)

Force

Force = the cause of acceleration or a change in velocity

- force is measured in units called Newtons

Net force = the combination of all the forces acting upon an object

bull The size of the arrow represents the amount of forcehellip

bull The arrows are the same so there is no movement

Friction

Friction = the force between two objects in contact that opposes the motion of either object

Pretend you are in a helicopter looking down on a ski slope in early springhellip The ice is meltinghellip Patches of dirt and gravel begin to showhellip

How much friction

Skis + snow = little frictionhellip skis move over snow

Skis + dirt = a lot of frictionhellip skis do not move over dirt

Air resistance is a type of friction

Gravity

Gravity = Force of attraction between 2 objects due to their masses

The force of gravity is different on different planets moons etc

On earth g = 98ms2

Gravity depends upon the masses as well as the distance between objects

Newtonrsquos Laws of Motion

Newtonrsquos 1st Law- the law of inertia

An object at rest remains at rest and an object in motion remains in motion unless it experiences an unbalanced force

bull Example 1 Whiplash ndash Person B is stopped at a traffic light Person A is not paying attention and rear-ends Person B

bull Result Person B moves forward suddenlyhellip Their head snaps back as it attempts to ldquoremain at restrdquo Their body attached to the seat moves forwardhellip their head snaps forward to catch up with the body resulting in whiplash

Example 2 Bus ride - The bus driver does not like children Every time they get too loud he slams on the breaks Why does he do this

Inertia = The tendency of an object to remain at rest or in motion with a constant velocity All objects have inertia because they resist changes in motion

Trivia If two people on a space ship (in space) get into a physical fight which will win

Person A Person B

Even though they are weightlesshellip there is no gravity Person A has a greater mass therefore a greater inertia

Newtonrsquos 2nd law of Motion- the law of acceleration

bull The unbalanced force acting on an object equals the objectrsquos mass times its acceleration

bull Force = Mass x Acceleration

Example pushing a cart

The greater the mass the more force needed to cause acceleration

Bumper cars

P = Mass x Velocity

- Measured in kgms

Momentum and ∆ Velocity

- large momentum difficult to change velocity

- small momentum easier to change velocity

Class Experiment Red light green light

Stationary objects have momentum of zero

Why No motion = no speed = no velocity = no momentum

Momentum is directly proportional to masshellip momentum increases as mass increases

P

Mass (kg)

Force

Force = the cause of acceleration or a change in velocity

- force is measured in units called Newtons

Net force = the combination of all the forces acting upon an object

bull The size of the arrow represents the amount of forcehellip

bull The arrows are the same so there is no movement

Friction

Friction = the force between two objects in contact that opposes the motion of either object

Pretend you are in a helicopter looking down on a ski slope in early springhellip The ice is meltinghellip Patches of dirt and gravel begin to showhellip

How much friction

Skis + snow = little frictionhellip skis move over snow

Skis + dirt = a lot of frictionhellip skis do not move over dirt

Air resistance is a type of friction

Gravity

Gravity = Force of attraction between 2 objects due to their masses

The force of gravity is different on different planets moons etc

On earth g = 98ms2

Gravity depends upon the masses as well as the distance between objects

Newtonrsquos Laws of Motion

Newtonrsquos 1st Law- the law of inertia

An object at rest remains at rest and an object in motion remains in motion unless it experiences an unbalanced force

bull Example 1 Whiplash ndash Person B is stopped at a traffic light Person A is not paying attention and rear-ends Person B

bull Result Person B moves forward suddenlyhellip Their head snaps back as it attempts to ldquoremain at restrdquo Their body attached to the seat moves forwardhellip their head snaps forward to catch up with the body resulting in whiplash

Example 2 Bus ride - The bus driver does not like children Every time they get too loud he slams on the breaks Why does he do this

Inertia = The tendency of an object to remain at rest or in motion with a constant velocity All objects have inertia because they resist changes in motion

Trivia If two people on a space ship (in space) get into a physical fight which will win

Person A Person B

Even though they are weightlesshellip there is no gravity Person A has a greater mass therefore a greater inertia

Newtonrsquos 2nd law of Motion- the law of acceleration

bull The unbalanced force acting on an object equals the objectrsquos mass times its acceleration

bull Force = Mass x Acceleration

Example pushing a cart

The greater the mass the more force needed to cause acceleration

Bumper cars

Momentum and ∆ Velocity

- large momentum difficult to change velocity

- small momentum easier to change velocity

Class Experiment Red light green light

Stationary objects have momentum of zero

Why No motion = no speed = no velocity = no momentum

Momentum is directly proportional to masshellip momentum increases as mass increases

P

Mass (kg)

Force

Force = the cause of acceleration or a change in velocity

- force is measured in units called Newtons

Net force = the combination of all the forces acting upon an object

bull The size of the arrow represents the amount of forcehellip

bull The arrows are the same so there is no movement

Friction

Friction = the force between two objects in contact that opposes the motion of either object

Pretend you are in a helicopter looking down on a ski slope in early springhellip The ice is meltinghellip Patches of dirt and gravel begin to showhellip

How much friction

Skis + snow = little frictionhellip skis move over snow

Skis + dirt = a lot of frictionhellip skis do not move over dirt

Air resistance is a type of friction

Gravity

Gravity = Force of attraction between 2 objects due to their masses

The force of gravity is different on different planets moons etc

On earth g = 98ms2

Gravity depends upon the masses as well as the distance between objects

Newtonrsquos Laws of Motion

Newtonrsquos 1st Law- the law of inertia

An object at rest remains at rest and an object in motion remains in motion unless it experiences an unbalanced force

bull Example 1 Whiplash ndash Person B is stopped at a traffic light Person A is not paying attention and rear-ends Person B

bull Result Person B moves forward suddenlyhellip Their head snaps back as it attempts to ldquoremain at restrdquo Their body attached to the seat moves forwardhellip their head snaps forward to catch up with the body resulting in whiplash

Example 2 Bus ride - The bus driver does not like children Every time they get too loud he slams on the breaks Why does he do this

Inertia = The tendency of an object to remain at rest or in motion with a constant velocity All objects have inertia because they resist changes in motion

Trivia If two people on a space ship (in space) get into a physical fight which will win

Person A Person B

Even though they are weightlesshellip there is no gravity Person A has a greater mass therefore a greater inertia

Newtonrsquos 2nd law of Motion- the law of acceleration

bull The unbalanced force acting on an object equals the objectrsquos mass times its acceleration

bull Force = Mass x Acceleration

Example pushing a cart

The greater the mass the more force needed to cause acceleration

Bumper cars

Momentum is directly proportional to masshellip momentum increases as mass increases

P

Mass (kg)

Force

Force = the cause of acceleration or a change in velocity

- force is measured in units called Newtons

Net force = the combination of all the forces acting upon an object

bull The size of the arrow represents the amount of forcehellip

bull The arrows are the same so there is no movement

Friction

Friction = the force between two objects in contact that opposes the motion of either object

Pretend you are in a helicopter looking down on a ski slope in early springhellip The ice is meltinghellip Patches of dirt and gravel begin to showhellip

How much friction

Skis + snow = little frictionhellip skis move over snow

Skis + dirt = a lot of frictionhellip skis do not move over dirt

Air resistance is a type of friction

Gravity

Gravity = Force of attraction between 2 objects due to their masses

The force of gravity is different on different planets moons etc

On earth g = 98ms2

Gravity depends upon the masses as well as the distance between objects

Newtonrsquos Laws of Motion

Newtonrsquos 1st Law- the law of inertia

An object at rest remains at rest and an object in motion remains in motion unless it experiences an unbalanced force

bull Example 1 Whiplash ndash Person B is stopped at a traffic light Person A is not paying attention and rear-ends Person B

bull Result Person B moves forward suddenlyhellip Their head snaps back as it attempts to ldquoremain at restrdquo Their body attached to the seat moves forwardhellip their head snaps forward to catch up with the body resulting in whiplash

Example 2 Bus ride - The bus driver does not like children Every time they get too loud he slams on the breaks Why does he do this

Inertia = The tendency of an object to remain at rest or in motion with a constant velocity All objects have inertia because they resist changes in motion

Trivia If two people on a space ship (in space) get into a physical fight which will win

Person A Person B

Even though they are weightlesshellip there is no gravity Person A has a greater mass therefore a greater inertia

Newtonrsquos 2nd law of Motion- the law of acceleration

bull The unbalanced force acting on an object equals the objectrsquos mass times its acceleration

bull Force = Mass x Acceleration

Example pushing a cart

The greater the mass the more force needed to cause acceleration

Bumper cars

Force

Force = the cause of acceleration or a change in velocity

- force is measured in units called Newtons

Net force = the combination of all the forces acting upon an object

bull The size of the arrow represents the amount of forcehellip

bull The arrows are the same so there is no movement

Friction

Friction = the force between two objects in contact that opposes the motion of either object

Pretend you are in a helicopter looking down on a ski slope in early springhellip The ice is meltinghellip Patches of dirt and gravel begin to showhellip

How much friction

Skis + snow = little frictionhellip skis move over snow

Skis + dirt = a lot of frictionhellip skis do not move over dirt

Air resistance is a type of friction

Gravity

Gravity = Force of attraction between 2 objects due to their masses

The force of gravity is different on different planets moons etc

On earth g = 98ms2

Gravity depends upon the masses as well as the distance between objects

Newtonrsquos Laws of Motion

Newtonrsquos 1st Law- the law of inertia

An object at rest remains at rest and an object in motion remains in motion unless it experiences an unbalanced force

bull Example 1 Whiplash ndash Person B is stopped at a traffic light Person A is not paying attention and rear-ends Person B

bull Result Person B moves forward suddenlyhellip Their head snaps back as it attempts to ldquoremain at restrdquo Their body attached to the seat moves forwardhellip their head snaps forward to catch up with the body resulting in whiplash

Example 2 Bus ride - The bus driver does not like children Every time they get too loud he slams on the breaks Why does he do this

Inertia = The tendency of an object to remain at rest or in motion with a constant velocity All objects have inertia because they resist changes in motion

Trivia If two people on a space ship (in space) get into a physical fight which will win

Person A Person B

Even though they are weightlesshellip there is no gravity Person A has a greater mass therefore a greater inertia

Newtonrsquos 2nd law of Motion- the law of acceleration

bull The unbalanced force acting on an object equals the objectrsquos mass times its acceleration

bull Force = Mass x Acceleration

Example pushing a cart

The greater the mass the more force needed to cause acceleration

Bumper cars

bull The size of the arrow represents the amount of forcehellip

bull The arrows are the same so there is no movement

Friction

Friction = the force between two objects in contact that opposes the motion of either object

Pretend you are in a helicopter looking down on a ski slope in early springhellip The ice is meltinghellip Patches of dirt and gravel begin to showhellip

How much friction

Skis + snow = little frictionhellip skis move over snow

Skis + dirt = a lot of frictionhellip skis do not move over dirt

Air resistance is a type of friction

Gravity

Gravity = Force of attraction between 2 objects due to their masses

The force of gravity is different on different planets moons etc

On earth g = 98ms2

Gravity depends upon the masses as well as the distance between objects

Newtonrsquos Laws of Motion

Newtonrsquos 1st Law- the law of inertia

An object at rest remains at rest and an object in motion remains in motion unless it experiences an unbalanced force

bull Example 1 Whiplash ndash Person B is stopped at a traffic light Person A is not paying attention and rear-ends Person B

bull Result Person B moves forward suddenlyhellip Their head snaps back as it attempts to ldquoremain at restrdquo Their body attached to the seat moves forwardhellip their head snaps forward to catch up with the body resulting in whiplash

Example 2 Bus ride - The bus driver does not like children Every time they get too loud he slams on the breaks Why does he do this

Inertia = The tendency of an object to remain at rest or in motion with a constant velocity All objects have inertia because they resist changes in motion

Trivia If two people on a space ship (in space) get into a physical fight which will win

Person A Person B

Even though they are weightlesshellip there is no gravity Person A has a greater mass therefore a greater inertia

Newtonrsquos 2nd law of Motion- the law of acceleration

bull The unbalanced force acting on an object equals the objectrsquos mass times its acceleration

bull Force = Mass x Acceleration

Example pushing a cart

The greater the mass the more force needed to cause acceleration

Bumper cars

Friction

Friction = the force between two objects in contact that opposes the motion of either object

Pretend you are in a helicopter looking down on a ski slope in early springhellip The ice is meltinghellip Patches of dirt and gravel begin to showhellip

How much friction

Skis + snow = little frictionhellip skis move over snow

Skis + dirt = a lot of frictionhellip skis do not move over dirt

Air resistance is a type of friction

Gravity

Gravity = Force of attraction between 2 objects due to their masses

The force of gravity is different on different planets moons etc

On earth g = 98ms2

Gravity depends upon the masses as well as the distance between objects

Newtonrsquos Laws of Motion

Newtonrsquos 1st Law- the law of inertia

An object at rest remains at rest and an object in motion remains in motion unless it experiences an unbalanced force

bull Example 1 Whiplash ndash Person B is stopped at a traffic light Person A is not paying attention and rear-ends Person B

bull Result Person B moves forward suddenlyhellip Their head snaps back as it attempts to ldquoremain at restrdquo Their body attached to the seat moves forwardhellip their head snaps forward to catch up with the body resulting in whiplash

Example 2 Bus ride - The bus driver does not like children Every time they get too loud he slams on the breaks Why does he do this

Inertia = The tendency of an object to remain at rest or in motion with a constant velocity All objects have inertia because they resist changes in motion

Trivia If two people on a space ship (in space) get into a physical fight which will win

Person A Person B

Even though they are weightlesshellip there is no gravity Person A has a greater mass therefore a greater inertia

Newtonrsquos 2nd law of Motion- the law of acceleration

bull The unbalanced force acting on an object equals the objectrsquos mass times its acceleration

bull Force = Mass x Acceleration

Example pushing a cart

The greater the mass the more force needed to cause acceleration

Bumper cars

How much friction

Skis + snow = little frictionhellip skis move over snow

Skis + dirt = a lot of frictionhellip skis do not move over dirt

Air resistance is a type of friction

Gravity

Gravity = Force of attraction between 2 objects due to their masses

The force of gravity is different on different planets moons etc

On earth g = 98ms2

Gravity depends upon the masses as well as the distance between objects

Newtonrsquos Laws of Motion

Newtonrsquos 1st Law- the law of inertia

An object at rest remains at rest and an object in motion remains in motion unless it experiences an unbalanced force

bull Example 1 Whiplash ndash Person B is stopped at a traffic light Person A is not paying attention and rear-ends Person B

bull Result Person B moves forward suddenlyhellip Their head snaps back as it attempts to ldquoremain at restrdquo Their body attached to the seat moves forwardhellip their head snaps forward to catch up with the body resulting in whiplash

Example 2 Bus ride - The bus driver does not like children Every time they get too loud he slams on the breaks Why does he do this

Inertia = The tendency of an object to remain at rest or in motion with a constant velocity All objects have inertia because they resist changes in motion

Trivia If two people on a space ship (in space) get into a physical fight which will win

Person A Person B

Even though they are weightlesshellip there is no gravity Person A has a greater mass therefore a greater inertia

Newtonrsquos 2nd law of Motion- the law of acceleration

bull The unbalanced force acting on an object equals the objectrsquos mass times its acceleration

bull Force = Mass x Acceleration

Example pushing a cart

The greater the mass the more force needed to cause acceleration

Bumper cars

Gravity

Gravity = Force of attraction between 2 objects due to their masses

The force of gravity is different on different planets moons etc

On earth g = 98ms2

Gravity depends upon the masses as well as the distance between objects

Newtonrsquos Laws of Motion

Newtonrsquos 1st Law- the law of inertia

An object at rest remains at rest and an object in motion remains in motion unless it experiences an unbalanced force

bull Example 1 Whiplash ndash Person B is stopped at a traffic light Person A is not paying attention and rear-ends Person B

bull Result Person B moves forward suddenlyhellip Their head snaps back as it attempts to ldquoremain at restrdquo Their body attached to the seat moves forwardhellip their head snaps forward to catch up with the body resulting in whiplash

Example 2 Bus ride - The bus driver does not like children Every time they get too loud he slams on the breaks Why does he do this

Inertia = The tendency of an object to remain at rest or in motion with a constant velocity All objects have inertia because they resist changes in motion

Trivia If two people on a space ship (in space) get into a physical fight which will win

Person A Person B

Even though they are weightlesshellip there is no gravity Person A has a greater mass therefore a greater inertia

Newtonrsquos 2nd law of Motion- the law of acceleration

bull The unbalanced force acting on an object equals the objectrsquos mass times its acceleration

bull Force = Mass x Acceleration

Example pushing a cart

The greater the mass the more force needed to cause acceleration

Bumper cars

Newtonrsquos Laws of Motion

Newtonrsquos 1st Law- the law of inertia

An object at rest remains at rest and an object in motion remains in motion unless it experiences an unbalanced force

bull Example 1 Whiplash ndash Person B is stopped at a traffic light Person A is not paying attention and rear-ends Person B

bull Result Person B moves forward suddenlyhellip Their head snaps back as it attempts to ldquoremain at restrdquo Their body attached to the seat moves forwardhellip their head snaps forward to catch up with the body resulting in whiplash

Example 2 Bus ride - The bus driver does not like children Every time they get too loud he slams on the breaks Why does he do this

Inertia = The tendency of an object to remain at rest or in motion with a constant velocity All objects have inertia because they resist changes in motion

Trivia If two people on a space ship (in space) get into a physical fight which will win

Person A Person B

Even though they are weightlesshellip there is no gravity Person A has a greater mass therefore a greater inertia

Newtonrsquos 2nd law of Motion- the law of acceleration

bull The unbalanced force acting on an object equals the objectrsquos mass times its acceleration

bull Force = Mass x Acceleration

Example pushing a cart

The greater the mass the more force needed to cause acceleration

Bumper cars

bull Example 1 Whiplash ndash Person B is stopped at a traffic light Person A is not paying attention and rear-ends Person B

bull Result Person B moves forward suddenlyhellip Their head snaps back as it attempts to ldquoremain at restrdquo Their body attached to the seat moves forwardhellip their head snaps forward to catch up with the body resulting in whiplash

Example 2 Bus ride - The bus driver does not like children Every time they get too loud he slams on the breaks Why does he do this

Inertia = The tendency of an object to remain at rest or in motion with a constant velocity All objects have inertia because they resist changes in motion

Trivia If two people on a space ship (in space) get into a physical fight which will win

Person A Person B

Even though they are weightlesshellip there is no gravity Person A has a greater mass therefore a greater inertia

Newtonrsquos 2nd law of Motion- the law of acceleration

bull The unbalanced force acting on an object equals the objectrsquos mass times its acceleration

bull Force = Mass x Acceleration

Example pushing a cart

The greater the mass the more force needed to cause acceleration

Bumper cars

bull Result Person B moves forward suddenlyhellip Their head snaps back as it attempts to ldquoremain at restrdquo Their body attached to the seat moves forwardhellip their head snaps forward to catch up with the body resulting in whiplash

Example 2 Bus ride - The bus driver does not like children Every time they get too loud he slams on the breaks Why does he do this

Inertia = The tendency of an object to remain at rest or in motion with a constant velocity All objects have inertia because they resist changes in motion

Trivia If two people on a space ship (in space) get into a physical fight which will win

Person A Person B

Even though they are weightlesshellip there is no gravity Person A has a greater mass therefore a greater inertia

Newtonrsquos 2nd law of Motion- the law of acceleration

bull The unbalanced force acting on an object equals the objectrsquos mass times its acceleration

bull Force = Mass x Acceleration

Example pushing a cart

The greater the mass the more force needed to cause acceleration

Bumper cars

Example 2 Bus ride - The bus driver does not like children Every time they get too loud he slams on the breaks Why does he do this

Inertia = The tendency of an object to remain at rest or in motion with a constant velocity All objects have inertia because they resist changes in motion

Trivia If two people on a space ship (in space) get into a physical fight which will win

Person A Person B

Even though they are weightlesshellip there is no gravity Person A has a greater mass therefore a greater inertia

Newtonrsquos 2nd law of Motion- the law of acceleration

bull The unbalanced force acting on an object equals the objectrsquos mass times its acceleration

bull Force = Mass x Acceleration

Example pushing a cart

The greater the mass the more force needed to cause acceleration

Bumper cars

Trivia If two people on a space ship (in space) get into a physical fight which will win

Person A Person B

Even though they are weightlesshellip there is no gravity Person A has a greater mass therefore a greater inertia

Newtonrsquos 2nd law of Motion- the law of acceleration

bull The unbalanced force acting on an object equals the objectrsquos mass times its acceleration

bull Force = Mass x Acceleration

Example pushing a cart

The greater the mass the more force needed to cause acceleration

Bumper cars

Newtonrsquos 2nd law of Motion- the law of acceleration

bull The unbalanced force acting on an object equals the objectrsquos mass times its acceleration

bull Force = Mass x Acceleration

Example pushing a cart

The greater the mass the more force needed to cause acceleration

Bumper cars

Example pushing a cart

The greater the mass the more force needed to cause acceleration

Bumper cars

Bumper cars

Newtonrsquos 3rd law of Motion- the law of interaction

bull For every action there is an opposite and equal reaction force

bull Forces occur in pairs

Example Holding up a wall

• Chapter 8
• Motion
• Slide 3
• Slide 4
• Speed
• Slide 6
• Slide 7
• Slide 8
• Slide 9
• Slide 10
• Velocity
• Slide 12
• Mathematical ndash Graphic Representations of Velocity
• Slide 14
• Slide 15
• Slide 16
• Graphing Velocity (Average Speed)
• Slide 18
• Slide 19
• Slide 20
• Slide 21
• Velocity Graphs and Profiles of Terrain
• Slide 23
• Dimensional Analysis ndash Unit Analysis
• Slide 25
• Slide 26
• Slide 27
• Slide 28
• Slide 29
• Slide 30
• Slide 31
• Slide 32
• Slide 33
• Slide 34
• Slide 35
• Slide 36
• Slide 37
• Acceleration
• Slide 39
• Slide 40
• Graphing Acceleration
• Slide 42
• Slide 43
• Comparing Velocity and Acceleration
• Slide 45
• Slide 46
• Slide 47
• Slide 48
• How it all fits together
• Momentum
• Slide 51
• Slide 52
• Slide 53
• Force
• Slide 55
• Slide 56
• Friction
• Slide 58
• Gravity
• Newtonrsquos Laws of Motion
• Slide 61
• Slide 62
• Slide 63
• Slide 64
• Slide 65
• Slide 66
• Slide 67
• Slide 68
• Slide 69
• Slide 70

Example Holding up a wall

• Chapter 8
• Motion
• Slide 3
• Slide 4
• Speed
• Slide 6
• Slide 7
• Slide 8
• Slide 9
• Slide 10
• Velocity
• Slide 12
• Mathematical ndash Graphic Representations of Velocity
• Slide 14
• Slide 15
• Slide 16
• Graphing Velocity (Average Speed)
• Slide 18
• Slide 19
• Slide 20
• Slide 21
• Velocity Graphs and Profiles of Terrain
• Slide 23
• Dimensional Analysis ndash Unit Analysis
• Slide 25
• Slide 26
• Slide 27
• Slide 28
• Slide 29
• Slide 30
• Slide 31
• Slide 32
• Slide 33
• Slide 34
• Slide 35
• Slide 36
• Slide 37
• Acceleration
• Slide 39
• Slide 40
• Graphing Acceleration
• Slide 42
• Slide 43
• Comparing Velocity and Acceleration
• Slide 45
• Slide 46
• Slide 47
• Slide 48
• How it all fits together
• Momentum
• Slide 51
• Slide 52
• Slide 53
• Force
• Slide 55
• Slide 56
• Friction
• Slide 58
• Gravity
• Newtonrsquos Laws of Motion
• Slide 61
• Slide 62
• Slide 63
• Slide 64
• Slide 65
• Slide 66
• Slide 67
• Slide 68
• Slide 69
• Slide 70