Motion - mikeprovost.weebly.commikeprovost.weebly.com/uploads/2/5/2/8/25282938/chapter_2-_motion... · • Motion occurs when an object changes its position relative to a reference

Motion

Section 3 • Acceleration

Section 1 • Describing Motion

Section 2 • Velocity and Momentum

Table of Contents

Section

1 Describing Motion

• Are distance and time important in describing running events at the track-and-field meets in the Olympics?

Motion

Comstock/JupiterImages

Section

1 Describing Motion

• Distance and time are important. In order to win a race, you must cover the distance in the shortest amount of time.

• How would you describe the motion of the runners in the race?

Motion


Section

1 Describing Motion

• You don't always need to see something move to know that motion has taken place.

• A reference point is needed to determine the position of an object.

Motion and Position

• Motion occurs when an object changes its position relative to a reference point.

• The motion of an object depends on the reference point that is chosen.

Section

1 Describing Motion

• An important part of describing the motion of an object is to describe how far it has moved, which is distance.

• The SI unit of length or distance is the meter (m). Longer distances are measured in kilometers (km).

Distance

Section

1 Describing Motion

Distance

• Shorter distances are measured in centimeters (cm).

Section

1 Describing Motion

• The runner travels 50 m in the original direction (north) plus 30 m in the opposite direction (south), so the total distance she ran is 80 m.

Displacement

• Suppose a runner jogs to the 50-m mark and then turns around and runs back to the 20-m mark.

Section

1 Describing Motion

• Displacement is the distance and direction of an object's change in position from the starting point.

Displacement

• Sometimes you may want to know not only your distance but also your direction from a reference point, such as from the starting point.

Section

1 Describing Motion

• The length of the runner's displacement and the distance traveled would be the same if the runner's motion was in a single direction.

Displacement

Section

1 Describing Motion

• Displacements in the same direction can be added.

Adding Displacements

• For example:

Section

1 Describing Motion

• Displacements in opposite directions can be subtracted.


• For example, if you walk 10 m east and then 5 m west, the size of your displacement is:

Section

1 Describing Motion

• Displacements that are not in the same direction or in opposite directions cannot be directly added or subtracted.


• For example, if you walk 4 m east and then 3 m north, your displacement is 5 m in a roughly northeast direction, but the total distance traveled is 7m.

Section

1 Describing Motion

• You could describe movement by the distance traveled and by the displacement from the starting point.

• You also might want to describe how fast it is moving.

Speed

• Speed is the distance an object travels per unit of time.

Section

1 Describing Motion

• Any change over time is called a rate.

• If you think of distance as the change in position, then speed is the rate at which distance is traveled or the rate of change in position.

Calculating Speed

Section

1 Describing Motion

Calculating Speed

• The SI unit for distance is the meter and the SI unit of time is the second (s), so in SI, units of speed are measured in meters per second (m/s).

Section

1 Describing Motion

• Sometimes it is more convenient to express speed in other units, such as kilometers per hour (km/h).

Calculating Speed

Section

1 Describing Motion

• Suppose you are in a car traveling on a nearly empty freeway. You look at the speedometer and see that the car's speed hardly changes.

• If you are traveling at a constant speed, you can measure your speed over any distance interval.

Motion with Constant Speed

Section

1 Describing Motion

• Usually speed is not constant.

Changing Speed

• Think about riding a bicycle for a distance of 5 km, as shown.

Section

1 Describing Motion

Changing Speed

• How would you express your speed on such a trip? Would you use your fastest speed, your slowest speed, or some speed between the two?

Section

1 Describing Motion

• Average speed describes speed of motion when speed is changing.

Average Speed

• Average speed is the total distance traveled divided by the total time of travel.

• If the total distance traveled was 5 km and the total time was 1/4 h, or 0.25 h. The average speed was:

Section

1 Describing Motion

• A speedometer shows how fast a car is going at one point in time or at one instant.

Instantaneous Speed

• The speed shown on a speedometer is the instantaneous speed. Instantaneous speed is the speed at a given point in time.

Ryan McGinnis/Getty Images

Section

1 Describing Motion

• When something is speeding up or slowing down, its instantaneous speed is changing.

Instantaneous Speed

• If an object is moving with constant speed, the instantaneous speed doesn't change.

Section

1 Describing Motion

• The motion of an object over a period of time can be shown on a distance-time graph.

Graphing Motion

• Time is plotted along the horizontal axis of the graph and the distance traveled is plotted along the vertical axis of the graph.

Click image to play movie

Section

1 Describing Motion

• On a distance-time graph, the distance is plotted on the vertical axis and the time on the horizontal axis.

Plotting a Distance-Time Graph

• Each axis must have a scale that covers the range of number to be plotted.

Section

1 Describing Motion

• Once the scales for each axis are in place, the data points can be plotted.

Plotting a Distance-Time Graph

• After plotting the data points, draw a line connecting the points.

Section

1

Question 1

What is the difference between distance and displacement?

Section Check

Section

1

Answer

Distance describes how far an object

moves; displacement is the distance

and the direction of an object’s

change in position.

Section Check

Section

1

Question 2

__________ is the distance an object travels per unit

of time.

A. acceleration

B. displacement

C. speed

D. velocity

Section Check

Section

1

Answer

The answer is C. Speed is the distance an object travels

per unit of time.

Section Check

Section

1

Answer

Instantaneous speed is the speed at a given point in time.

Question 3

What is instantaneous speed?

Section Check

Section

2 Velocity and Momentum

• Speed describes only how fast something is moving.

Velocity

• To determine direction you need to know the velocity.

• Velocity includes the speed of an object and the direction of its motion.

Section


• Because velocity depends on direction as well as speed, the velocity of an object can change even if the speed of the object remains constant.

Velocity

• The speed of this car might be constant, but its velocity is not constant because the direction of motion is always changing.

Section


• As you look around the surface of the Earth from year to year, the basic structure of the planet seems the same.

Motion of Earth's Crust

• Yet if you examined geological evidence of what Earth's surface looked like over the past 250 million years, you would see that large changes have occurred.

Section


Motion of Earth's Crust

Click the

play

button to

see how

the

continents

have

moved

over time.

626_Fig_8.swf

Section


• These moving plates cause geological changes such as the formation of mountain ranges, earthquakes and volcanic eruptions.

Moving Continents

• The movement of the plates also is changing the size of the oceans and the shapes of the continents.

Section


• If you are sitting in a chair reading this sentence, you are moving.

• You are not moving relative to your desk or your school building, but you are moving relative to the other planets in the solar system and the Sun.

Relative Motion

Section


• The choice of a reference point influences how you describe the motion of an object.

• For example, consider a hurricane that is moving towards your house as you evacuate.

Relative Motion

Section


• If you choose your house as a reference point, the hurricane appears to be approaching at 20 km/h and the car appears to be moving away at 10 km/h.

Relative Motion

Section


• If you choose your car as a reference point, the hurricane appears to be approaching at 10 km/h and the car appears to be moving away at 10 km/h.

Relative Motion

Section


Momentum

• A moving object has a property called momentum that is related to how much force is needed to change its motion.

• The momentum of an object is the product of its mass and velocity.

Section


Momentum

• Momentum is given the symbol p and can be calculated with the following equation:

• The unit for momentum is kg · m/s. Notice that momentum has a direction because velocity has a direction.

Section


Momentum

• When two objects have the same velocity, the object with the larger mass has the larger momentum.

• For example, a 1,500-kg car traveling at 30 m/s east has a momentum of 45,000 kg•m/s east.

Section


Momentum

• But a 30,000-kg truck traveling at 30 m/s east has a momentum of 900,000 kg•m/s.

• Furthermore, when two objects have the same mass, the one with the larger velocity has a larger momentum.

Section

2

Question 1

A 1,500-kg car is traveling west at 100 m/s. What is the car’s momentum?

A. 1,500 kg•m/s

B. 150,000 kg•m/s

C. 1,400 kg•m/s

D. 1,600 kg•m/s

Section Check

Section

2

Answer

The answer is B. Momentum is the product of the object’s mass and velocity: 1,500 kg × 100 m/s = 150,000 kg•m/s

Section Check

Section

2

Question 2

A. mass, acceleration

B. mass, velocity

C. mass, weight

D. net force, velocity

The momentum of an object is the product of its

__________ and __________.

Section Check

Section

2

Answer

The correct answer is B. An object’s momentum

is the product of its mass and velocity, and is

given the symbol p.

Section Check

Section

2

Question 3

________ is the speed and direction of an object’s motion.

A. Displacement

B. Motion

C. Velocity

D. Position

Section Check

Section

2

Answer

The answer is C. Velocity includes an object’s speed and

the direction of its motion.

Section Check

Section

3 Acceleration

Acceleration, Speed and Velocity

• Acceleration is the rate of change of velocity. When the velocity of an object changes, the object is accelerating.

• A change in velocity can be either a change in how fast something is moving, or a change in the direction it is moving.

• Acceleration occurs when an object changes its speed, its direction, or both.

Section

3 Acceleration

Speeding Up and Slowing Down

• When you think of acceleration, you probably think of something speeding up. However, an object that is slowing down also is accelerating.

• Acceleration also has direction, just as velocity does.

• A change in velocity can be either a change in how fast something is moving or a change in the direction of movement.

Section

3 Acceleration


• If the acceleration is in the same direction as the velocity, the speed increases.

Section

3 Acceleration


• If the speed decreases, the acceleration is in the opposite direction from the velocity, and the acceleration is negative.

Section

3 Acceleration

Changing Direction

• Any time a moving object changes direction, its velocity changes and it is accelerating.

Section

3 Acceleration

Speed-time Graphs

• For objects traveling in a straight line, a speed-time graph can provide information about the object’s acceleration.

• The slope of the line on a speed-time graph equals the object’s acceleration.

Section

3 Acceleration

Calculating Acceleration

• To calculate the acceleration of an object, the change in velocity is divided by the length of time interval over which the change occurred.

• To calculate the change in velocity, subtract the initial velocity—the velocity at the beginning of the time interval—from the final velocity—the velocity at the end of the time interval.

Section

3 Acceleration


• Then the change in velocity is:

Section

3 Acceleration


• Using this expression for the change in velocity, the acceleration can be calculated from the following equation:

Section

3 Acceleration


• If the direction of motion doesn't change and the object moves in a straight line, the size of change in velocity is the same as the change in speed.

• The size of change in velocity then is the final speed minus the initial speed.

Section

3 Acceleration

Speeding Up

• Suppose a jet airliner starts at rest at the end of a runway and reaches a velocity of 80 m/s east in 20 s.

David Frazier/Corbis

Section

3 Acceleration

Speeding Up

• The airliner is traveling in a straight line down the runway, so its speed and velocity are the same size.

• Because it started from rest, its initial speed was zero.

Section

3 Acceleration

Speeding Up

• Its acceleration can be calculated as follows:

Section

3 Acceleration

Slowing Down

• The final speed is zero and the initial speed was 3 m/s.

• Now imagine that a skateboarder is moving in a straight line with a velocity of 3 m/s and north comes to a stop in 2 s.

Ken Karp for MMH

Section

3 Acceleration

Calculating Negative Acceleration

• The skateboarder's acceleration is calculated as follows:

• The acceleration is in the opposite direction of the skateboard’s velocity when the skateboarder is slowing down.

Section

3 Acceleration

Motion in Two Dimensions

• When an object changes direction, it is accelerating.

• Most objects do not move in only in straight lines.

• Like displacement and velocity, accelerations in the same direction can be added and accelerations in opposite directions can be subtracted.

• Accelerations that are not in the same direction or in opposite directions cannot be directly added together.

Section

3 Acceleration

Changing Direction

• The speed of the horses in this carousel is constant, but the horses are accelerating because their direction is changing constantly.

Section

3 Acceleration

• When a ball enters a curve, even if its speed does not change, it is accelerating because its direction is changing.

Circular Motion

• When a ball goes around a curve, the change in the direction of the velocity is toward the center of the curve.

Section

3 Acceleration

• Acceleration toward the center of a curved or circular path is called centripetal acceleration.

Circular Motion

Section

3 Acceleration

• If you’ve tossed a ball to someone, you’ve probably noticed that thrown objects don’t always travel in straight lines. They curve downward.

Projectile Motion

• Earth’s gravity causes projectiles to follow a curved path.

Section

3 Acceleration

• When you throw a ball, the force exerted by your hand pushes the ball forward.

Horizontal and Vertical Motions

• This force gives the ball horizontal motion.

Donald Miralle/Getty Images

• No force accelerates it forward, so its horizontal velocity is constant, if you ignore air resistance.

Section

3 Acceleration

• However, when you let go of the ball, gravity can pull it downward, giving it vertical motion.


• The ball has constant horizontal velocity but increasing vertical velocity.

Section

3 Acceleration

• Gravity exerts an unbalanced force on the ball, changing the direction of its path from only forward to forward and downward.


• The result of these two motions is that the ball appears to travel in a curve.

Section

3 Acceleration

• If you were to throw a ball as hard as you could from shoulder height in a perfectly horizontal direction, would it take longer to reach the ground than if you dropped a ball from the same height?

Horizontal and Vertical Distance

Click image to view movie

Section

3 Acceleration

• Surprisingly, it wouldn’t.

Horizontal and Vertical Distance

• Both balls travel the same vertical distance in the same amount of time.

Section

3 Acceleration

Amusement Park Acceleration

• Engineers use the laws of physics to design amusement park rides that are thrilling, but harmless.

• The highest speeds and accelerations usually are produced on steel roller coasters.

CORBIS

Section

3 Acceleration


• Steel roller coasters can offer multiple steep drops and inversion loops, which give the rider large accelerations.

• As the rider moves down a steep hill or an inversion loop, he or she will accelerate toward the ground due to gravity.

Section

3 Acceleration


• When riders go around a sharp turn, they also are accelerated.

• This acceleration makes them feel as if a force is pushing them toward the side of the car.

Section

3

Question 1

Acceleration is the rate of change of __________.

Section Check

Section

3

Answer

The correct answer is velocity. Acceleration occurs

when an object changes its speed, direction, or both.

Section Check

Section

3

Question 2

Which is NOT a form of acceleration?

A. maintaining a constant speed and direction

B. speeding up

C. slowing down

D. turning

Section Check

Section

3

Answer

The answer is A. Any change of speed or direction

results in acceleration.

Section Check

Section

3

Question 3

What is the acceleration of a hockey player who is

skating at 10 m/s east and comes to a complete stop in

2 s?

A. 5 m/s2 east

B. 5 m/s2 west

C. 20 m/s2 east

D. 20 m/s2 west

Section Check

Section

3

Answer

The answer is B. Calculate acceleration by subtracting

initial velocity (10 m/s) from final velocity (0), then

dividing by the time interval (2s).

Section Check

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Chapter Resources

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Chapter Summary

Chapter Review Questions

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THUMBNAILS

Athlete Running


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Conversion Table

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Distance vs. Displacement

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THUMBNAILS

Units of Speed

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THUMBNAILS

Displacement

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Speed Changing over Distance

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Speedometer

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Graphing Motion

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Positive Acceleration

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Negative Acceleration

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Changing Direction

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Changing Direction

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Positive Acceleration

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Negative Acceleration

Ken Karp for MMH

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CORBIS

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Circular Motion

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Pitcher

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Speed-Time Graph

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Relative Motion

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626_Fig_8.swf

• Motion is a change of position of a body. Distance is the measure of how far an object moved. Displacement is the distance and direction of an object's change in position from the starting point.

Describing Motion

• A reference point must be specified in order to determine an object's position.

Reviewing Main Ideas

• The speed of an object can be calculated from this equation:

Describing Motion

• Velocity describes the speed and direction of a moving object.

• The slope of a line on a distance-time graph is equal to the speed.


• Momentum is the product of an object’s mass and velocity.

Velocity and Momentum

• Velocity describes the speed and direction of a moving object.


• Acceleration occurs when an object changes speed or changes direction.

Acceleration

• An object speeds up if its acceleration is in the direction of its motion.

• An object slows down if its acceleration is opposite to the direction of its motion.

• Acceleration is the rate of change of velocity, and is calculated from this equation:


Question 1

A. displacement

B. distance

C. instantaneous speed

D. velocity

Which includes both the speed of a moving object and the

direction of its motion?

Chapter Review

Answer

The answer is D. Displacement includes direction, but not

speed.

Chapter Review

Question 2

A. 6.67 m/s

B. 1.85 m/s

C. 0.93 m/s

D. 0.85 m/s

What is the average speed in m/s of a runner who travels

10.0 km in 1.5 hours?

Chapter Review

Answer

The answer is B. Remember to convert kilometers to

meters and hours to seconds.

Chapter Review

Question 3

A car travels at a constant speed of 40 m/s for 2 hours.

What was the distance traveled in km?

Chapter Review

Answer

The car traveled 288 km. There are 3,600 s in 1 h and

1,000 m in 1 km.

Step 1: 40 m/s × 7,200 = 288,000

Step 2: 288,000= 288 km

1,000

Chapter Review

Question 1

A. 165 m/s

B. 55 m/s

C. 30 m/s

D. 15 m/s

A moving object traveled 4900 m in 165 s. What is its

average speed?


Answer

The answer is C. Average speed is equal to the total

distance traveled divided by the total time of travel.


Question 2

This graph represents

swim times for three

different swimmers.

Which swimmer did not

maintain a constant

speed?


A. A

B. B

C. C

D. All speeds were constant.


Answer

The answer is C. During the time interval between 10

and 20 minutes, swimmer C had a speed of 0 m/min.


Question 3

A. 3 m/s2 South

B. 3 m/s2 North

C. 20 m/s2 South

D. 20 m/s2 North

Calculate the acceleration of a car that starts at rest and

has a final velocity of 30 m/s north after 10 s.


Answer

The answer is B. Use this equation to calculate

acceleration: a = (vf – vi)/t


Question 4

A. 42.5 km South

B. 127.5 km South

Car A is traveling north at 85 km/h. After 1 hour, the car

turns around 180º and travels at the same speed for 1.5

hours. What is the car’s displacement at the end of the

trip?

C. 212.5 km South

D. 42.5 km North


Answer

The answer is A, 42.5 km South. During the first hour the

car traveled 85 km North. During the second hour, the car

traveled 127.5 km South. Even though the total distance

traveled is 212.5 km, the car is 42.5 km South of its

starting point.


Question 5

What is Bill’s average speed?

Runner Distance

(km)

Time (min)

Carlos 14.5 42

Bill 8.0 38

Janet 12.4 32

Ann 10.3 30


A. .10 km/min

B. .21 km/min

C. .34 km/min

D. .38 km/min

Runner Distance

(km)

Time (min)

Carlos 14.5 42

Bill 8.0 38

Janet 12.4 32

Ann 10.3 30


Answer

The correct answer is B. Use the equation:


Help

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