chapter 4 linear motion - whs physics

Chapter 4

Linear Motion

You can describe the

motion of an object by

its position, speed,

direction, and

acceleration.

I. Motion Is Relative (2.1)

A. Everything moves. Even things that appear

to be at rest move.

1. Motion is described by motion

relative to something else.

a. Relative to the sun, the

center of the galaxy, etc.

b. We will discus motion

(things in our environment)

relative to the surface of the

Earth.

II. Speed (4.2)

A. Speed is measure of how fast something is

moving (rate at which distance is covered)

1. Rate– term used to describe

something divided by time.

2. Speed = Units of distance / units of

time (distance covered per unit of time)

3. Common Units

a. miles/hour (mi/h)

b. kilometers/hour (km/h)

c. meters/second (m/s) Used in physics

•Continental drift: 2 mm/year (1mm = one

millimeter = 10-3 meters)

•Walking speed: 3 miles/hour = 4.4 feet/second =

1.3 m/s (1m = 1 meter, s = seconds)

•Driving speed: 60 miles/hr = 100 km/hr = 88 ft/s =

26 m/s

•Orbital speed (near Earth orbit) = 8 km/s = 17,000

miles/hr

•Earth's speed around the sun = 30 km/s

•Speed of light = 300,000 km/s = 186,000 miles/s.

B. Instantaneous Speed– the speed at any instant

(What you see on a car’s speedometer)

C. Average Speed– total distance covered/time

interval

1. Does not indicate variations in speed over

time.

2. still describes rate at which distance

traveled

Average speed =Time interval

Total distance covered

01

01

tt

dd

t

dv

think!

If a cheetah can maintain a constant speed of 25 m/s, it will

cover 25 meters every second. At this rate, how far will it

travel in 10 seconds? In 1 minute?

4.2 Speed

think!

If a cheetah can maintain a constant speed of 25 m/s, it will

cover 25 meters every second. At this rate, how far will it

travel in 10 seconds? In 1 minute?

Answer: In 10 s the cheetah will cover 250 m, and in 1 min

(or 60 s) it will cover 1500 m.

4.2 Speed

think!

The speedometer in every car also has an

odometer that records the distance traveled. If the

odometer reads zero at the beginning of a trip and

35 km a half hour later, what is the average speed?

4.2 Speed

think!

The speedometer in every car also has an

odometer that records the distance traveled. If the

odometer reads zero at the beginning of a trip and

35 km a half hour later, what is the average speed?

Answer:

4.2 Speed

D. Velocity (4.3)

1. Velocity and speed are often used

interchangeably, but in physics are different.

a. Velocity is speed in a given direction.

b. Speed is how fast object moves

(direction does not matter)

E. Constant Velocity– must have constant speed

and direction

1. Object moves in straight line

2. Object’s path does not curve

F. Changing Velocity

1. Velocity will change if either speed or

direction changes.

2. Constant speed and constant velocity are

not the same.

think!

The speedometer of a car moving northward reads 60 km/h.

It passes another car that travels southward at 60 km/h. Do

both cars have the same speed? Do they have the same

velocity?

4.3 Velocity

think!

The speedometer of a car moving northward reads 60 km/h.

It passes another car that travels southward at 60 km/h. Do

both cars have the same speed? Do they have the same

velocity?

Answer: Both cars have the same speed, but they have

opposite velocities because they are moving in opposite

directions.

4.3 Velocity

III. Acceleration (4.4)

A. acceleration is the rate at which the

velocity is changing

1. applies to increases as

well as decreases in velocity.

2. decrease in velocity often

called deceleration or

negative acceleration

Acceleration =Time interval

Change of velocity

01

01

tt

vv

t

va

B. Acceleration applies to changes in direction as

well as speed

1. When motion is in straight line the term

speed and velocity are often used

interchangeably.

1. When motion is in straight line the term speed

and velocity are often used interchangeably.

Acceleration along a straight line =Change of speed

Time interval

2. Units for acceleration a bit more complicated

Acceleration =Change of speed

Time interval 210

1

/10

s

m

s

sm

Accelerate in the direction of velocity–speed up

4.4 Acceleration


Accelerate against velocity–slow down

4.4 Acceleration


Accelerate against velocity–slow down

Accelerate at an angle to velocity–change direction

4.4 Acceleration

think!

Suppose a car moving in a straight line steadily increases

its speed each second, first from 35 to 40 km/h, then from

40 to 45 km/h, then from 45 to 50 km/h. What is its

acceleration?

4.4 Acceleration

think!

Suppose a car moving in a straight line steadily increases

its speed each second, first from 35 to 40 km/h, then from

40 to 45 km/h, then from 45 to 50 km/h. What is its

acceleration?

Answer: The speed increases by 5 km/h during each 1-s

interval in a straight line. The acceleration is therefore

5 km/h•s during each interval.

4.4 Acceleration

think!

In 5 seconds a car moving in a straight line increases its

speed from 50 km/h to 65 km/h, while a truck goes from rest

to 15 km/h in a straight line. Which undergoes greater

acceleration? What is the acceleration of each vehicle?

4.4 Acceleration

think!

In 5 seconds a car moving in a straight line increases its

speed from 50 km/h to 65 km/h, while a truck goes from rest

to 15 km/h in a straight line. Which undergoes greater

acceleration? What is the acceleration of each vehicle?

Answer: The car and truck both increase their speed by

15 km/h during the same time interval, so their acceleration

is the same.

4.4 Acceleration

IV. Free Fall: How Fast (4.5)

A. The force of Gravity causes object to

accelerate downward

1. If we disregard air resistance

(air friction) then free falling

objects only affected by gravity.

Called free fall

2. Use letter (g) to represent

gravity

3. gravity varies slightly around the

Earth. Average value is about

10 m/s2

4. More accurately, g is 9.8 m/s2

B. The instantaneous speed of an object falling from

rest is equal to the acceleration multiplied by the

amount of time it falls.

Instantaneous speed = acceleration x elapsed time

(v symbolizes both speed and velocity)

gtv

1. speed decreases at the same rate with an object

moving upwards as it increases when moving

downward

2. An object thrown upward will reach a velocity of

zero when it gets to its highest point

V. Free Fall: How Far (4.6)

A. Relationship between distance

traveled, acceleration, and

velocity

gtv 2

2

1gtd

g

dt

2

Rearrange and

solve for t

think!

During the span of the second time interval in Table 4.2,

the object begins at 10 m/s and ends at 20 m/s. What is

the average speed of the object during this 1-second

interval? What is its acceleration?

4.5 Free Fall: How Fast

think!

During the span of the second time interval in Table 4.2,

the object begins at 10 m/s and ends at 20 m/s. What is

the average speed of the object during this 1-second

interval? What is its acceleration?

Answer: The average speed is 15 m/s. The acceleration

is 10 m/s2.


think!

What would the speedometer reading on the falling rock

be 4.5 seconds after it drops from rest?

How about 8 seconds after it is dropped?


think!

What would the speedometer reading on the falling rock

be 4.5 seconds after it drops from rest?

How about 8 seconds after it is dropped?

Answer: The speedometer readings would be 45 m/s and

80 m/s, respectively.


VI. Graphs of Motion

A. Equations and tables not the only way to

describe relationships such as velocity and

acceleration.

1. Linear relationship- e.g. speed and

time

a. Forms straight line curve.

b. Has constant slope (direct

proportion)

2. Parabolic relationship– e.g. distance versus

time

a. Not straight line. Curved line

b. Tangent at any point gives slope at that

point (slope of this curve is instantaneous

speed. Remember that slope is rise/run or

change in y over change in x.

Distance/time = speed

VII. Air Resistance and Falling Objects (4.8)

A. Air resistance noticeably alters

the motion of things (like feathers,

paper, etc.)

B. Less effect on more dense

(compact) objects

C. Air resistance is small enough

to be neglected in most cases.

VIII. How Fast, How Far, How Quickly. How Fast

Changes (4.9)

A. speed and velocity-used to describe how

fast something free falls from rest.

equation to use: gtv

gtvv 0

B. To specify how far the object has fallen we are

talking about distance.

equation to use:2

2

1gtd

What is this graph telling us?

Change in velocity over time = acceleration

C. Acceleration– how quickly does speed or velocity

change

1. Very complex concept

2. rate of a rate

Constant Positive Velocity

Constant Negative Velocity

Positive Velocity and Positive Acceleration

Positive Velocity and Negative Acceleration

Motion Diagram

Standing still

Moving constant speed

Speeding up

Slowing down

Motion Diagram

•Particle Model

•Replace object with single point

•Simplified version of motion diagram

Standing still

Moving constant speed

Speeding up

Slowing down

•

• • • • •

•• • • •

• • • ••

Particle Model

1. Jake walks east through a passenger car on a train that moves 10

m/s in the same direction. Jake’s speed relative to the car is 2 m/s.

Jake’s speed relative to an observer at rest outside the train is

a. 2 m/s.

b. 5 m/s.

c. 8 m/s.

d. 12 m/s.

Assessment Questions

1. Jake walks east through a passenger car on a train that moves 10

m/s in the same direction. Jake’s speed relative to the car is 2 m/s.

Jake’s speed relative to an observer at rest outside the train is

a. 2 m/s.

b. 5 m/s.

c. 8 m/s.

d. 12 m/s.

Answer: D


2. A gazelle travels 2 km in a half hour. The gazelle’s average speed is

a. 1/2 km/h.

b. 1 km/h.

c. 2 km/h.

d. 4 km/h.


2. A gazelle travels 2 km in a half hour. The gazelle’s average speed is

a. 1/2 km/h.

b. 1 km/h.

c. 2 km/h.

d. 4 km/h.

Answer: D


3. Constant speed in a constant direction is

a. constant velocity.

b. constant acceleration.

c. instantaneous speed.

d. average velocity.


3. Constant speed in a constant direction is

a. constant velocity.

b. constant acceleration.

c. instantaneous speed.

d. average velocity.

Answer: A


4. A vehicle undergoes acceleration when it

a. gains speed.

b. decreases speed.

c. changes direction.

d. all of the above


4. A vehicle undergoes acceleration when it

a. gains speed.

b. decreases speed.

c. changes direction.

d. all of the above

Answer: D


5. If a falling object gains 10 m/s each second it

falls, its acceleration can be expressed as

a. 10 m/s/s.

b. 10 m/s2.

c. v = gt.

d. both A and B.


5. If a falling object gains 10 m/s each second it

falls, its acceleration can be expressed as

a. 10 m/s/s.

b. 10 m/s2.

c. v = gt.

d. both A and B.

Answer: D


6. A rock falls 180 m from a cliff into the ocean. How long is it in free

fall?

a. 6 s

b. 10 s

c. 18 s

d. 180 s


6. A rock falls 180 m from a cliff into the ocean. How long is it in free

fall?

a. 6 s

b. 10 s

c. 18 s

d. 180 s

Answer: A


7. The slope of a speed-versus-time graph represents

a. distance traveled.

b. velocity.

c. acceleration.

d. air resistance.


7. The slope of a speed-versus-time graph represents

a. distance traveled.

b. velocity.

c. acceleration.

d. air resistance.

Answer: C


8. In a vacuum tube, a feather is seen to fall as fast as a coin. This is

because

a. gravity doesn’t act in a vacuum.

b. air resistance doesn’t act in a vacuum.

c. greater air resistance acts on the coin.

d. gravity is greater in a vacuum.


8. In a vacuum tube, a feather is seen to fall as fast as a coin. This is

because

a. gravity doesn’t act in a vacuum.

b. air resistance doesn’t act in a vacuum.

c. greater air resistance acts on the coin.

d. gravity is greater in a vacuum.

Answer: B


9. Speed and acceleration are actually

a. one and the same concept, but expressed differently.

b. rates of one another.

c. entirely different concepts.

d. expressions of distance traveled.


9. Speed and acceleration are actually

a. one and the same concept, but expressed differently.

b. rates of one another.

c. entirely different concepts.

d. expressions of distance traveled.

Answer: C


chapter 4 linear motion - whs physics

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