Chapter 11: MotionChapter 11: Motion

Section 11.1 – Distance and Section 11.1 – Distance and DisplacementDisplacement

To describe To describe motionmotion accurately and accurately and completely, a completely, a frame of referenceframe of reference is is necessary.necessary.

A A frame of referenceframe of reference is a system of is a system of objects that are objects that are not movingnot moving with with respect to one another.respect to one another.

Relative motionRelative motion is movement in is movement in relation to a relation to a frame of referenceframe of reference..

Are the people in the cars moving?Are the people in the cars moving?

DistanceDistanceDistanceDistance is the length of a is the length of a pathpath between two points.between two points.

It is helpful to express It is helpful to express distancesdistances in in units that are best suited to the units that are best suited to the motionmotion you are studying. you are studying.

DistanceDistance

What unit would you use to measure What unit would you use to measure the length of someone’s hair?the length of someone’s hair?

What unit would you use to measure What unit would you use to measure from McDonough to Atlanta?from McDonough to Atlanta?

What unit would you use to measure What unit would you use to measure the length of a room?the length of a room?

Centimeters (cm)

Kilometers (km)

Meters (m)

DisplacementDisplacementDisplacementDisplacement is the direction from is the direction from the starting point and the length of a the starting point and the length of a straight linestraight line from the starting point from the starting point to the to the ending pointending point..

Combining DisplacementsCombining Displacements

DisplacementDisplacement is a is a vectorvector..

A A vectorvector is a quantity that has is a quantity that has magnitude and magnitude and directiondirection..

Add displacements using Add displacements using vector vector additionaddition..

Combining DisplacementsCombining DisplacementsWhen two When two displacementsdisplacements, , represented by two vectors, have the represented by two vectors, have the same directionsame direction, you can , you can addadd their their magnitudes.magnitudes.

If two If two displacementsdisplacements have have opposite opposite directionsdirections, the magnitudes , the magnitudes subtractsubtract from each other.from each other.

Distance vs. DisplacementDistance vs. Displacement

Section 11.1 AssessmentSection 11.1 Assessment

1.1. What is a frame of reference? How What is a frame of reference? How is it used to measure motion?is it used to measure motion?

2.2. How are distance and displacement How are distance and displacement similar and different?similar and different?

3.3. Would you measure the height of a Would you measure the height of a building in meters? Why or why building in meters? Why or why not?not?

Section 11.2 – Speed and VelocitySection 11.2 – Speed and Velocity

SpeedSpeed is the ratio of the is the ratio of the distancedistance an an object moves to the amount of object moves to the amount of timetime the object moves.the object moves.

The The SI unitSI unit of speed is of speed is meters per meters per second (m/s).second (m/s).

Average SpeedAverage Speed

Average speedAverage speed is the is the total distancetotal distance traveled (d) divided by the traveled (d) divided by the timetime (t) it (t) it takes to travel the distance.takes to travel the distance.

Average speed = Average speed = total distancetotal distance

total timetotal time

Sample ProblemsSample Problems

While traveling on vacation, you While traveling on vacation, you measure the times and distances measure the times and distances traveled. You travel 35km in 0.4hr, traveled. You travel 35km in 0.4hr, followed by 53km in 0.6hr. What is followed by 53km in 0.6hr. What is your average speed?your average speed?

Total distance = 35km + 53km = 88kmTotal time = 0.4hr + 0.6hr

S = d = 88km = 88km/hr88km/hr t 1hr

Sample ProblemsSample ProblemsA person jogs 4.0km in 32min, then A person jogs 4.0km in 32min, then 2.0km in 22min, and finally 1.0km in 2.0km in 22min, and finally 1.0km in 16min. What is the jogger’s average 16min. What is the jogger’s average speed?speed?

A train travels 190km in 3.0hr, and A train travels 190km in 3.0hr, and then 120km in 2.0hr. What is its then 120km in 2.0hr. What is its average speed?average speed?

d = 4.0km + 2.0km + 1.0km = 7.0km s = d = 7.0km = 0.10km/min0.10km/mint = 32min + 22min + 16min = 70min t 70min

d = 190km + 120km = 310km s = d = 310km = 62km/hr62km/hrt = 3.0hr + 2.0hr = 5.0hr t 5.0hr

Instantaneous SpeedInstantaneous Speed

Instantaneous speedInstantaneous speed is the rate at is the rate at which an object if moving at a given which an object if moving at a given momentmoment in time. in time.

For example, you can describe the For example, you can describe the instantaneous speedinstantaneous speed of a car by of a car by looking at the looking at the speedometerspeedometer..

Graphing motionGraphing motion

The The slopeslope of a line on a of a line on a distance-timedistance-time graph is graph is speedspeed..

Graphing motionGraphing motion

The The steepersteeper the slope of the line, the slope of the line, then then fasterfaster the speed. the speed.

Straight linesStraight lines represent constant represent constant speedspeed..

VelocityVelocityVelocityVelocity is a description of both is a description of both speed and speed and directiondirection. Velocity is a . Velocity is a vectorvector..

A change in velocity can be a result A change in velocity can be a result of a of a change in speed, direction, or change in speed, direction, or bothboth..

Combining velocitiesCombining velocities

Two or more Two or more velocitiesvelocities add by add by vector vector additionaddition..

Section 11.2 AssessmentSection 11.2 Assessment

1.1. What does velocity describe?What does velocity describe?

2.2. What shows the speed on a What shows the speed on a distance-time graph?distance-time graph?

3.3. What is the difference between What is the difference between average speed and instantaneous average speed and instantaneous speed?speed?

4.4. How can two or more velocities by How can two or more velocities by combined?combined?

Section 11.2 AssessmentSection 11.2 Assessment

5. Does a car’s speedometer show 5. Does a car’s speedometer show instantaneous speed, average speed, instantaneous speed, average speed, or velocity? Explain.or velocity? Explain.

6. A plane’s average speed between 6. A plane’s average speed between two cities is 600km/hr. If the trip two cities is 600km/hr. If the trip takes 2.5hr, how far did the plane takes 2.5hr, how far did the plane fly?fly?

s = d d = s x t d = 600km x 2.5hr = 1500km1500km t hr

Section 11.3 - AccelerationSection 11.3 - Acceleration

The rate at which The rate at which velocityvelocity changes is changes is called called accelerationacceleration..

AccelerationAcceleration can be described as can be described as changes in changes in speedspeed, changes in , changes in directiondirection, or changes in, or changes in

bothboth..

Changes in SpeedChanges in Speed

AccelerationAcceleration can be either an can be either an increaseincrease or a or a decreasedecrease in speed. in speed.

DecelerationDeceleration is an acceleration that is an acceleration that slowsslows an object’s speed. an object’s speed.

Free FallFree FallFree fallFree fall is the movement of an is the movement of an object toward the Earth solely object toward the Earth solely because of because of gravitygravity..

Objects falling near Objects falling near Earth’s surfaceEarth’s surface accelerate downward at a rate of accelerate downward at a rate of 9.8m/s9.8m/s22..

Changes in DirectionChanges in Direction

Although you may have a constant Although you may have a constant speedspeed, a change in , a change in directiondirection means means you are you are acceleratingaccelerating..

Constant AccelerationConstant Acceleration

Constant accelerationConstant acceleration is a steady is a steady change in change in velocityvelocity. That is, the . That is, the velocityvelocity changes by the same changes by the same amount each amount each secondsecond..

AccelerationAccelerationYou calculate You calculate accelerationacceleration for for straight-line motion by dividing the straight-line motion by dividing the change in velocitychange in velocity by the by the total timetotal time..The The SI unitSI unit for acceleration is for acceleration is m/sm/s22..

Acceleration = Acceleration = change in velocitychange in velocity total timetotal time

a = a = vvff – v – vii

tt

Sample ProblemsSample Problems

A ball rolls down a ramp, starting A ball rolls down a ramp, starting from rest. After 2 seconds, its from rest. After 2 seconds, its velocity is 6m/s. What is the velocity is 6m/s. What is the acceleration of the ball?acceleration of the ball?

vf = 6m/s a = vf – vi = 6m/s – 0m/s = 3m/s3m/s22

vi = 0m/s t 2st = 2s

Sample ProblemsSample Problems

A car traveling at 10m/s starts to A car traveling at 10m/s starts to decelerate steadily. It comes to a decelerate steadily. It comes to a complete stop in 20s. What is its complete stop in 20s. What is its acceleration?acceleration?

An airplane travels down a runway An airplane travels down a runway for 4.0s with an acceleration of for 4.0s with an acceleration of 9.0m/s9.0m/s22. What is its change in . What is its change in velocity during this time?velocity during this time?

vi = 10m/s a = vf – vi = 0m/s – 10m/s = -0.5m/s-0.5m/s22

vf = 0m/s t 20s t = 20s

a = 9.0m/s2 a = vf – vi vf – vi = a x t = 9.0m x 4.0s = 36m/s 36m/s t = 4.0s t s2

Graphs of AccelerationGraphs of Acceleration

The The slopeslope of a of a speed-timespeed-time graph is graph is accelerationacceleration..

Constant accelerationConstant acceleration is represented is represented by a by a straight linestraight line..

Graphs of AccelerationGraphs of AccelerationA A horizontal linehorizontal line represents constant represents constant speedspeed..

If the If the slopeslope of a line is of a line is negativenegative, then , then the object is the object is slowing downslowing down..

AccelerationAcceleration

On a On a distance-timedistance-time graph, graph, accelerationacceleration is represented by a is represented by a curved linecurved line..

Instantaneous AccelerationInstantaneous Acceleration

Instantaneous accelerationInstantaneous acceleration is how is how fast a velocity is changing at a fast a velocity is changing at a specific instantspecific instant..

Section 11.3 AssessmentSection 11.3 Assessment

1.1. Describe three types of changes in Describe three types of changes in velocity.velocity.

2.2. What is the equation for What is the equation for acceleration?acceleration?

3.3. What shows acceleration on a What shows acceleration on a speed-time graph?speed-time graph?

4.4. Define instantaneous acceleration.Define instantaneous acceleration.

5.5. How are deceleration and How are deceleration and acceleration related?acceleration related?

Section 11.3 AssessmentSection 11.3 Assessment

6. A train moves from rest to a speed 6. A train moves from rest to a speed of 25m/s in 30.0s. What is the of 25m/s in 30.0s. What is the magnitude of its acceleration?magnitude of its acceleration?

7. A car traveling at a speed of 25m/s 7. A car traveling at a speed of 25m/s increases its speed to 30m/s in 10s. increases its speed to 30m/s in 10s. What is its acceleration?What is its acceleration?

vf = 25m/s a = vf – vi = 25m/s – 0m/s = 0.83m/s0.83m/s22

vi = 0m/s t 30s t = 30s

vf = 30m/s a = vf – vi = 30m/s – 25m/s = 0.5m/s0.5m/s22

vi = 25m/s t 10st = 10s

THE ENDTHE END