Chapter 2 Practice Problems, Review, and Assessment
Section 1 Force and Motion: Review
1. MAIN IDEA How does a motion diagram represent an object’s motion?
SOLUTION: A motion diagram shows the positions of a moving object at equal time intervals.
2. Motion Diagram of a Bike Rider Draw a particle model motion diagram for a bike rider moving at a constant pace along a straight path.
SOLUTION: Each dot represents the position of the bike rider at each time interval. The elapsed times between the
dots are equal. The equal spacing indicates that the bike rider moved an equal distance during each time
interval. Therefore, the rate of motion of the bike rider was constant.
3. Motion Diagram of a Car Draw a particle model motion diagram corresponding to the motion diagram in Figure 4
for a car coming to a stop at a stop sign. What point on the car did you use to represent the car?
SOLUTION: The point should be close to the center of the car.
As the car slowed down as it moved to the left, the distance it traveled during each equal time interval
became less and less. 4. Motion Diagram of a Bird Draw a particle model motion diagram corresponding to the motion diagram in
Figure 5 for a flying bird. What point on the bird did you choose to represent the bird?
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The point should be close to the center of the car.
As the car slowed down as it moved to the left, the distance it traveled during each equal time interval
Chapter
2 Practice Problems, Review, and Assessment
became less and less. 4. Motion Diagram of a Bird Draw a particle model motion diagram corresponding to the motion diagram in
Figure 5 for a flying bird. What point on the bird did you choose to represent the bird?
SOLUTION: The point should be close to the center of the bird. The equal distances between the dots indicates that
the bird was flying at a constant speed.
5. Critical Thinking Draw particle model motion diagrams for two runners during a race in which the first runner
crosses the finish line as the other runner is three-fourths of the way to the finish line.
SOLUTION: The greater distance between the dots for Runner 1 indicates that Runner 1 traveled a greater distance
than Runner 2 during each equal time interval.
Section 2 Where and When: Review
6. MAIN IDEA Identify a coordinate system you could use to describe the motion of a girl swimming across a
rectangular pool.
SOLUTION: Answers will vary. Sample answer: The position direction could be along the length of the pool. The
origin could be at one of the short sides of the pool.
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7. Displacement The motion diagram for a car traveling on an interstate highway is shown. The starting and ending
points are indicated.
The greater distance between the dots for Runner 1 indicates that Runner 1 traveled a greater distance
Chapter
Practice
Problems,
andinterval.
Assessment
than 2Runner
2 during
eachReview,
equal time
Section 2 Where and When: Review
6. MAIN IDEA Identify a coordinate system you could use to describe the motion of a girl swimming across a
rectangular pool.
SOLUTION: Answers will vary. Sample answer: The position direction could be along the length of the pool. The
origin could be at one of the short sides of the pool.
7. Displacement The motion diagram for a car traveling on an interstate highway is shown. The starting and ending
points are indicated.
Start ● ● ● ● ● ● End
Make a copy of the diagram. Draw a vector to represent the car’s displacement from the starting time to the end of the
third time interval.
SOLUTION: The length of the arrow indicates the distance the car traveled during three time intervals. The equal
distances between the hash marks indicates that the car traveled at a constant speed.
8. Position Two students add a vector for a moving object's position at t = 2 s to a motion diagram. When they compared their diagrams, they found that their vectors did not point in the same direction. Explain.
SOLUTION: A position vector goes from the origin to the object. When the origins are different, the position vectors
are different. On the other hand, a displacement vector has nothing to do with the origin.
9. Displacement The motion diagram for a boy walking to school is shown. Make a copy of this motion diagram, and draw vectors to represent the displacement between each pair of dots.
Home ● ● ● ● ● ● ● ● ● ● School
SOLUTION: The equal lengths of the arrows indicate that the boy walked at a constant speed. 10. Critical Thinking A car travels straight along a street from a grocery store to a post office. To represent its
motion,
you
use a coordinate
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positive direction. Your friend uses a coordinate system with its origin at the post office and the opposite direction
as the positive direction. Would the two of you agree on the car’s position? Displacement? Distance? The time
SOLUTION: The equal
lengths
of the arrows
indicate
that the boy walked at a constant speed. Chapter
2 Practice
Problems,
Review,
and Assessment
10. Critical Thinking A car travels straight along a street from a grocery store to a post office. To represent its
motion, you use a coordinate system with its origin at the grocery store and the direction the car is moving as the
positive direction. Your friend uses a coordinate system with its origin at the post office and the opposite direction
as the positive direction. Would the two of you agree on the car’s position? Displacement? Distance? The time
interval the trip took? Explain.
SOLUTION: The two students should agree on the displacement, distance, and time interval for the trip because
these three quantities are independent of where the origin of the coordinate system is placed. The two
students would not agree on the car’s position because the position is measured from the origin of the
coordinate system to the location of the car.
Section 3 Position-Time Graphs: Practice Problems
For problems 11-13, refer to Figure 12.
11. The graph in Figure 12 represents the motion of a car moving along a straight highway. Describe in words the
car’s motion.
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The car begins at a position of 125.0 m and moves toward the origin, arriving at the origin 5.0 s after it begins moving. The car continues beyond the origin. The two students should agree on the displacement, distance, and time interval for the trip because
these three quantities are independent of where the origin of the coordinate system is placed. The two
students would not agree on the car’s position because the position is measured from the origin of the
Chapter
2 Practice
Problems,
Review,ofand
coordinate
system
to the location
the Assessment
car.
Section 3 Position-Time Graphs: Practice Problems
For problems 11-13, refer to Figure 12.
11. The graph in Figure 12 represents the motion of a car moving along a straight highway. Describe in words the
car’s motion.
SOLUTION: The car begins at a position of 125.0 m and moves toward the origin, arriving at the origin 5.0 s after it begins moving. The car continues beyond the origin. 12. Draw a particle model motion diagram that corresponds to the graph.
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The car begins at a position of 125.0 m and moves toward the origin, arriving at the origin 5.0 s after it begins moving. The car continues beyond the origin. Chapter 2 Practice Problems, Review, and Assessment
12. Draw a particle model motion diagram that corresponds to the graph.
SOLUTION: The equal distances between the dots indicates the car moved toward the origin at a constant speed.
13. Answer the following questions about the car’s motion. Assume that the positive x-direction is east of the origin and
the negative x-direction is west of the origin.
a. At what time was the car's position 25.0 m east of the origin?
b. Where was the car at time t = 1.0 s?
c. What was the displacement of the car between times t = 1.0 s and t = 3.0 s?
SOLUTION: a. at 4.0 s Basic graph-reading skills are used to establish the relationship between the position of the
car and the elapsed time.
b. 100.0 m Basic graph-reading skills are used to establish the relationship between the position of the
car and the elapsed time.
c. 50.0 m Basic graph-reading skills are used to establish the relationship between the position of the
car and the elapsed time.
14. The graph in Figure 13 represents the motion of two pedestrians who are walking along a straight sidewalk in a
city. Describe in words the motion of the pedestrians. Assume that the positive direction is east of the origin.
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car and the elapsed time.
c. 50.0 m Basic graph-reading skills are used to establish the relationship between the position of the
Chapter
2 Practice
Problems,
car and
the elapsed
time. Review, and Assessment
14. The graph in Figure 13 represents the motion of two pedestrians who are walking along a straight sidewalk in a
city. Describe in words the motion of the pedestrians. Assume that the positive direction is east of the origin.
SOLUTION: The pedestrians walk the same distance during each time interval,and they both walk east the entire
time. Pedestrian A starts west of the origin, walks toward the origin, and continues walking east.
Pedestrian B starts at the origin and walks east.
The eqaul slopes of the parallel lines show that the two pedestrians walked at the same speed in the
same direction. 15. CHALLENGE Ari walked down the hall at school from the cafeteria to the band room, a distance of 100.0 m. A class of physics students recorded and graphed his position every 2.0 s, noting that he moved 2.6 m every 2.0 s. When was Ari at the following positions?
a. 25.0 m from the cafeteria
b. 25.0 m from the band room
c. Create a graph showing Ari’s motion.
SOLUTION: a. 19 s Ari's speed was 1.3 m/s. 25 m ÷ 1.3 m/s = 19 s b. 58 s At 25 m from the band room, Ari was 75 m from the cafeteria. 75 m ÷ 1.3 m/s = 58 s
c.
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Pedestrian B starts at the origin and walks east.
The eqaul slopes of the parallel lines show that the two pedestrians walked at the same speed in the
Chapter
2 Practice Problems, Review, and Assessment
same direction. 15. CHALLENGE Ari walked down the hall at school from the cafeteria to the band room, a distance of 100.0 m. A class of physics students recorded and graphed his position every 2.0 s, noting that he moved 2.6 m every 2.0 s. When was Ari at the following positions?
a. 25.0 m from the cafeteria
b. 25.0 m from the band room
c. Create a graph showing Ari’s motion.
SOLUTION: a. 19 s Ari's speed was 1.3 m/s. 25 m ÷ 1.3 m/s = 19 s b. 58 s At 25 m from the band room, Ari was 75 m from the cafeteria. 75 m ÷ 1.3 m/s = 58 s
c.
For problems 16–19, refer to the following graph: 16. Where was runner A located at t = 0 s?
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SOLUTION: Runner A passed the origin. Line A begins at point (0, 0).
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Chapter
2 Practice Problems, Review, and Assessment
For problems 16–19, refer to the following graph: 16. Where was runner A located at t = 0 s?
SOLUTION: Runner A passed the origin. Line A begins at point (0, 0).
17. Which runner was ahead at t = 48.0 s?
SOLUTION: Runner B was ahead at t = 48.0 s. At 45.0 s, the two runners were the same distance from the origin. At
that point the lines of the graph crossed, indicating that Runner B was beginning to be farther from the
origin than Runner A.
18. When Runner A was at 0.0 m, where was Runner B?
SOLUTION: at –50.0 m
The graph shows that Runner B started 50.0 m behind Runner A, who started at the origin.
19. How far apart were runners A and B at t = 20.0 s?
SOLUTION: approximately
30bymCognero
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30 m is the difference in the y coordinates of the runners at x = 20 s.
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SOLUTION: at –50.0 m
Chapter
2 Practice
Problems,
Review,
and Assessment
The graph
shows
that Runner
B started
50.0 m behind Runner A, who started at the origin.
19. How far apart were runners A and B at t = 20.0 s?
SOLUTION: approximately 30 m
30 m is the difference in the y coordinates of the runners at x = 20 s.
20. CHALLENGE Juanita goes for a walk. Later her friend Heather starts to walk after her. Their motions are
represented by the position-time graph in Figure 15.
a. How long had Juanita been walking when Heather started her walk
b. Will Heather catch up to Juanita? How can you tell?
c. What was Juanita’s position at t = 0.2 h?
d. At what time was Heather 5.0 km from the start?
SOLUTION: a. 6.0 min The graph shows that Heather joined the walk 0.1 h after Juanita started. 0.1 × 60 min = 6 min.
b. No, the lines representing Juanita’s and Heather’s motions get farther apart as time increases.
The lines will not intersect.
c. 1.0 km At x = 0.2 h, y = 1.0 km.
d. t = 1.8 h At y = 5.0 km, x = 1.8 h
Section 3 Position-Time Graph: Review
21. MAIN IDEA Using the particle model motion diagram in Figure 16 of a baby crawling across a kitchen floor,
plot a position-time graph to represent the baby’s motion. The time interval between successive dots on the
diagram is 1 s.
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The lines will not intersect.
c. 1.0 km At x = 0.2 h, y = 1.0 km.
d. t = 1.8 h At y = 5.0 km, x = 1.8 h
Chapter 2 Practice Problems, Review, and Assessment
Section 3 Position-Time Graph: Review
21. MAIN IDEA Using the particle model motion diagram in Figure 16 of a baby crawling across a kitchen floor,
plot a position-time graph to represent the baby’s motion. The time interval between successive dots on the
diagram is 1 s.
SOLUTION: The straight line formed by the dots indicate the baby crawled at a constant speed. The positive slope of
the line of dots shows that the baby was crawling in the "positive" direction away from the origin.
For problems 22–25, refer to Figure 17.
22. Particle Model Create a particle model motion diagram from the position-time graph in Figure 17 of a hockey
puck gliding across a frozen pond.
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The straight line formed by the dots indicate the baby crawled at a constant speed. The positive slope of
Chapter
2 Practice
Problems,
Review,
the line
of dots shows
that the
baby and
was Assessment
crawling in the "positive" direction away from the origin.
For problems 22–25, refer to Figure 17.
22. Particle Model Create a particle model motion diagram from the position-time graph in Figure 17 of a hockey
puck gliding across a frozen pond.
SOLUTION: The equal spacing between the dots indicates the puck moved at a constant speed.
23. Time Use the hockey puck’s position-time graph to determine the time when the puck was 10.0 m beyond the origin.
SOLUTION: 0.5 s
Across the time-axis, the time interval between the dots is 1 second. The reading of 10 meters up the
position-axis corresponds to 0.5 s on the time-axis.
24. Distance Use the position-time graph in Figure 17 to determine how far the hockey puck moved between times
0.0 s and 5.0 s.
SOLUTION: 100 m
The difference between the positions at time = 0 and time = 5 s is 100 m.
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25. Time Interval Use the position-time graph for the hockey puck to determine how much time it took for the puck to
0.5 s
Across the time-axis, the time interval between the dots is 1 second. The reading of 10 meters up the
Chapter
2 Practice
Problems, Review,
and
Assessment
position-axis
corresponds
to 0.5 s on
the
time-axis.
24. Distance Use the position-time graph in Figure 17 to determine how far the hockey puck moved between times
0.0 s and 5.0 s.
SOLUTION: 100 m
The difference between the positions at time = 0 and time = 5 s is 100 m.
25. Time Interval Use the position-time graph for the hockey puck to determine how much time it took for the puck to
go from 40 m beyond the origin to 80 m beyond the origin.
SOLUTION: 2.0 s
The difference between the Time at Position = 40 m and Position = 80 m is 4.0 s – 2.0 s = 2.0 s. 26. Critical Thinking Look at the particle model diagram and the position-time graph shown in Figure 18. Do they
describe the same motion? How do you know? Do not confuse the position coordinate system in the particle model
with the horizontal axis in the position-time graph. The time intervals in the particle model diagram are 2 s.
SOLUTION: No, they don’t describe the same motion. Although both objects are traveling in the positive direction,
one is moving more quickly than the other. Students can cite a number of different specific examples
from the graph and particle model to back this up. For example, the particle model shows a position of 2
m after
2 -s,Powered
but the
eSolutions
Manual
by graph
Cogneroshows a position of 8 m after 2 s.
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Section 4 How Fast: Practice Problems
SOLUTION: 2.0 s
Chapter
2 Practice between
Problems,
Assessment
The difference
theReview,
Time atand
Position
= 40 m and Position = 80 m is 4.0 s – 2.0 s = 2.0 s. 26. Critical Thinking Look at the particle model diagram and the position-time graph shown in Figure 18. Do they
describe the same motion? How do you know? Do not confuse the position coordinate system in the particle model
with the horizontal axis in the position-time graph. The time intervals in the particle model diagram are 2 s.
SOLUTION: No, they don’t describe the same motion. Although both objects are traveling in the positive direction,
one is moving more quickly than the other. Students can cite a number of different specific examples
from the graph and particle model to back this up. For example, the particle model shows a position of 2
m after 2 s, but the graph shows a position of 8 m after 2 s.
Section 4 How Fast: Practice Problems
27. The graph in Figure 21 describes the motion of a cruise ship drifting slowly through calm waters. The positive xdirection (along the vertical axis) is defined to be south.
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No, they don’t describe the same motion. Although both objects are traveling in the positive direction,
one is moving more quickly than the other. Students can cite a number of different specific examples
from the graph and particle model to back this up. For example, the particle model shows a position of 2
Chapter
2 Practice
Review,
and Assessment
m after
2 s, but Problems,
the graph shows
a position
of 8 m after 2 s.
Section 4 How Fast: Practice Problems
27. The graph in Figure 21 describes the motion of a cruise ship drifting slowly through calm waters. The positive xdirection (along the vertical axis) is defined to be south.
a. What is the ship’s average speed?
b. What is its average velocity?
SOLUTION: a. Using the points (0 s, 0 m) and (3 s, –1 m)
b. The average velocity is the slope of the line, including the sign, so it is –0.3 m/s or 0.3 m/s north.
28. Describe, in words, the cruise ship’s motion in the previous problem.
SOLUTION: The ship is moving north at a speed of 0.3 m/s.
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The ship's direction of motion and its speed describe the ship's velocity.
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b. The average velocity is the slope of the line, including the sign, so it is –0.3 m/s or 0.3 m/s north.
Chapter
2 Practice Problems, Review, and Assessment
28. Describe, in words, the cruise ship’s motion in the previous problem.
SOLUTION: The ship is moving north at a speed of 0.3 m/s.
The ship's direction of motion and its speed describe the ship's velocity.
29. What is the average velocity of an object that moves from 6.5 cm to 3.7 cm relative to the origin in 2.3 s?
SOLUTION: 30. The graph in Figure 22 represents the motion of a bicycle.
a. What is the bicycle’s average speed
b. What is its average velocity?
SOLUTION: a. What is the bicycle’s average speed
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Chapter 2 Practice Problems, Review, and Assessment
30. The graph in Figure 22 represents the motion of a bicycle.
a. What is the bicycle’s average speed
b. What is its average velocity?
SOLUTION: a. What is the bicycle’s average speed
b. What is its average velocity?
31. Describe, in words, the bicycle’s motion in the previous problem.
SOLUTION: The bicycle is moving in the positive direction at a speed of 0.7 km/min.
This is the description of the bicycle's velocity.
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32. CHALLENGE When Marshall takes his pet dog for a walk, the dog walks at a very consistent pace of
0.55 m/s. Draw a motion diagram and a position-time graph to represent Marshall’s dog walking the 19.8-
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Chapter 2 Practice Problems, Review, and Assessment
31. Describe, in words, the bicycle’s motion in the previous problem.
SOLUTION: The bicycle is moving in the positive direction at a speed of 0.7 km/min.
This is the description of the bicycle's velocity.
32. CHALLENGE When Marshall takes his pet dog for a walk, the dog walks at a very consistent pace of
0.55 m/s. Draw a motion diagram and a position-time graph to represent Marshall’s dog walking the 19.8m distance from in front of his house to the nearest stop sign.
SOLUTION: For problems 33–36, refer to Figure 24.
33. The diagram shows the path of a ship that sails at a constant velocity of 42 km/h east. What is the ship’s position
when it reaches point C, relative to the starting point, A, if it sails from point B to point C in exactly 1.5 h?
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Chapter 2 Practice Problems, Review, and Assessment
For problems 33–36, refer to Figure 24.
33. The diagram shows the path of a ship that sails at a constant velocity of 42 km/h east. What is the ship’s position
when it reaches point C, relative to the starting point, A, if it sails from point B to point C in exactly 1.5 h?
SOLUTION: 34. Another ship starts at the same time from point B, but its average velocity is 58 km/h east. What is its position, relative to A, after 1.5 h?
SOLUTION: 35. What would a ship’s position be if that ship started at point B and traveled at an average velocity of 35 km/h west to point D in a time period of 1.2 h?
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Chapter 2 Practice Problems, Review, and Assessment
35. What would a ship’s position be if that ship started at point B and traveled at an average velocity of 35 km/h west to point D in a time period of 1.2 h?
SOLUTION: 36. CHALLENGE Suppose two ships start from point B and travel west. One ship travels at an average velocity of
35 km/h for 2.2 h. Another ship travels at an average velocity of 26 km/h for 2.5 h. What is the final position of each ship?
SOLUTION: Section 4 How Fast: Review
37. MAIN IDEA How is an object’s velocity related to its position?
SOLUTION: An object’s velocity is the rate of change in its position.
For problems 38–40, refer to Figure 25.
38. Ranking Task Rank the position-time graphs according to the average speed, from greatest average speed to least
average speed. Specifically indicate any ties.
SOLUTION: Even though no numbers are known, you can compare the speeds using the slopes of the lines. For
speed, use the absolute value of the slope. Slope is rise over run.
vA = |–6 / 3| = 2
vB ≈ |5 / 3.3| ≈ 1.5
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vC = |–5 / 5| = 1
vD = |5 / 5| =1
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37. MAIN IDEA How is an object’s velocity related to its position?
SOLUTION: An object’s velocity is the rate of change in its position.
Chapter
2 Practice Problems, Review, and Assessment
For problems 38–40, refer to Figure 25.
38. Ranking Task Rank the position-time graphs according to the average speed, from greatest average speed to least
average speed. Specifically indicate any ties.
SOLUTION: Even though no numbers are known, you can compare the speeds using the slopes of the lines. For
speed, use the absolute value of the slope. Slope is rise over run.
vA = |–6 / 3| = 2
vB ≈ |5 / 3.3| ≈ 1.5
vC = |–5 / 5| = 1
vD = |5 / 5| =1
Therefore, the average speed from greatest to least is A, B, C = D.
39. Contrast Average Velocities Describe differences in the average velocities shown on the graph for objects A
and B. Describe differences in the average velocities shown on the graph for objects C and D.
SOLUTION: The magnitude of the average velocity of B is slightly greater than that of A, but the average velocity of
A is negative, and the average velocity of B is positive. The magnitudes of the average velocities of C
and D are equal, but the average velocity of D is positive, and the average velocity of C is negative.
40. Ranking Task Rank the graphs in Figure 25 according to each object’s initial position, from most positive
position to most negative position. Specifically indicate any ties. Would your ranking be different if you ranked
according to initial distance from the origin?
SOLUTION: A, C, B, D. Yes, the ranking from greatest to least distance would be A, C, D, B.
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41. Average
Velocity Explain how average speed and average velocity are related to eachPage 21
other for an object in uniform motion.
SOLUTION: Chapter
2 Practice Problems, Review, and Assessment
A, C, B, D. Yes, the ranking from greatest to least distance would be A, C, D, B.
41. Average Speed and Average Velocity Explain how average speed and average velocity are related to each
other for an object in uniform motion.
SOLUTION: Average speed is the absolute value of the average velocity if an object is in uniform motion.
42. Position Two cars are traveling along a straight road, as shown in Figure 26. They pass each other at point B
and then continue in opposite directions. The red car travels for 0.25 h from point B to point C at a constant
velocity of 32 km/h east. The blue car travels for 0.25 h from point B to point D at a constant velocity of
48 km/h west. How far has each car traveled from point B? What is the position of each car relative to the origin,
point A?
SOLUTION: 43. Position A car travels north along a straight highway at an average speed of 85 km/h. After driving 2.0 km, the car
passes a gas station and continues along the highway. What is the car’s position relative to the start of its trip 0.25 h after it passes the gas station?
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SOLUTION: Page 22
Chapter
2 Practice Problems, Review, and Assessment
43. Position A car travels north along a straight highway at an average speed of 85 km/h. After driving 2.0 km, the car
passes a gas station and continues along the highway. What is the car’s position relative to the start of its trip 0.25 h after it passes the gas station?
SOLUTION: 44. Critical Thinking In solving a physics problem, why is it important to create pictorial and physical models before
trying to solve an equation?
SOLUTION: Answers will vary. Drawing models helps you organize the problem situation. It is difficult to write the
proper equation if you don't have a clear picture of how things are situated and/or moving. Also, you
choose the coordinate system in this step, and this is essential in making sure you use the proper signs
on the quantities you will substitute into the equation later.
Chapter Assessment
Section 1 Picturing Motion: Mastering Concepts
45. What is the purpose of drawing a motion diagram?
SOLUTION: A motion diagram gives you a picture of motion that helps you visualize displacement and velocity.
46. Under what circumstances is it legitimate to treat an object as a particle when solving motion problems?
SOLUTION: An object can be treated as a point particle if internal motions are not important and if the object is small
in comparison to the distance it moves.
Chapter Assessment
Section 2 Where and When? Mastering Concepts
47. The following quantities describe location or its change: position, distance, and displacement. Briefly describe the
differences among them.
SOLUTION: Position and displacement are different from distance because position and displacement both contain
information about the direction in which an object has moved, but distance does not. Distance and eSolutions Manual - Powered by Cognero
displacement are different from position because they describe how an object’s location has changedPage 23
during a time interval, but position indicates exactly where an object is located at a precise time.
SOLUTION: An object can be treated as a point particle if internal motions are not important and if the object is small
Chapter
2 Practice to
Problems,
Review,
and Assessment
in comparison
the distance
it moves.
Chapter Assessment
Section 2 Where and When? Mastering Concepts
47. The following quantities describe location or its change: position, distance, and displacement. Briefly describe the
differences among them.
SOLUTION: Position and displacement are different from distance because position and displacement both contain
information about the direction in which an object has moved, but distance does not. Distance and displacement are different from position because they describe how an object’s location has changed
during a time interval, but position indicates exactly where an object is located at a precise time.
48. How can you use a clock to find a time interval?
SOLUTION: Read the clock at the beginning and end of the interval and subtract the beginning time from the ending
time.
Chapter Assessment
Section 3 Position-Time Graphs: Mastering Concepts
49. In-line Skating How can you use the position-time graphs for two in-line skaters to determine if and when one inline skater will pass the other one?
SOLUTION: Draw the two graphs on the same set of axes. One in-line skater will pass the other if the lines
representing each of their motions intersect. The time coordinate of the point where the lines intersect
is the time at which the passing occurs.
Chapter Assessment
Section 4 How Fast: Mastering Concepts
50. BIG IDEA Which equation describes how the average velocity of a moving object relates to its displacement?
SOLUTION: 51. Walking Versus Running A walker and a runner leave your front door at the same time. They move in the same
Page 24
velocities. Describe the position-time graphs of each.
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direction
SOLUTION: SOLUTION: Chapter
2 Practice Problems, Review, and Assessment
51. Walking Versus Running A walker and a runner leave your front door at the same time. They move in the same
direction at different constant velocities. Describe the position-time graphs of each.
SOLUTION: The slope of a position-time graph represents the speed of a moving object. A steeper slope indicates a
greater speed.
Both are straight lines that start at the same position, but the slope of the runner’s line is steeper.
52. What does the slope of a position-time graph measure?
SOLUTION: velocity
53. If you know the time it took an object to travel between two points and the positions of the object at the points, can
you determine the object's instantaneous velocity? Its average velocity? Explain.
SOLUTION: It is possible to calculate the average velocity from the information given, but it is not possible to find the
instantaneous velocity.
Chapter Assessment
Section 4 How Fast: Mastering Problems
54. You ride a bike at a constant speed of 4.0 m/s for 5.0 s. How far do you travel? (Level 1)
SOLUTION: 8 55. Astronomy Light from the Sun reaches Earth in about 8.3 min. The speed of light is 3.00×10 m/s. What is the
distance from the Sun to Earth? (Level 1)
SOLUTION: 56. Problem Posing Complete this problem so that someone must solve it using the concept of average speed: “A
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butterfly travels 15 m from one flower to another….” (Level 2)
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Chapter 2 Practice Problems, Review, and Assessment
56. Problem Posing Complete this problem so that someone must solve it using the concept of average speed: “A
butterfly travels 15 m from one flower to another….” (Level 2)
SOLUTION: Possible Answer: "If it takes the butterfly 7 seconds, what is its average speed?"
57. Nora jogs several times a week and always keeps track of how much time she runs each time she goes out. One
day she forgets to take her stopwatch with her and wonders if there is a way she can still have some idea of her
time. As she passes a particular bank building, she remembers that it is 4.3 km from her house. She knows from her previous training that she has a consistent pace of 4.0 m/s. How long has Nora been jogging when she reaches the bank? (Level 2)
SOLUTION: 58. Driving You and a friend each drive 50.0 km. You travel at 90.0 km/h; your friend travels at 95.0 km/h. How much
sooner will your friend finish the trip? (Level 3)
SOLUTION: Chapter Assessment: Applying Concepts
59. Ranking Task The position-time graph in Figure 27 shows the motion of four cows walking from the pasture
back to the barn. Rank the cows according to their average velocity, from slowest to fastest.
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Chapter 2 Practice Problems, Review, and Assessment
Chapter Assessment: Applying Concepts
59. Ranking Task The position-time graph in Figure 27 shows the motion of four cows walking from the pasture
back to the barn. Rank the cows according to their average velocity, from slowest to fastest.
SOLUTION: Moolinda, Dolly, Bessie, Elsie
60. Figure 28 is a position-time graph for a rabbit running away from a dog. How would the graph differ if the rabbit
ran twice as fast? How would it differ if the rabbit ran in the opposite direction?
SOLUTION: If the rabbit ran twice as fast, the slope of the graph would be twice as steep. If the rabbit ran in the
opposite direction, the magnitude of the slope would be the same, but it would be negative.
61. Test the following combinations and explain why each does not have the properties needed to describe the concept
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of velocity: Δx + Δt, Δx − Δt, Δx × Δt, Δt/Δx.
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SOLUTION: If the rabbit ran twice as fast, the slope of the graph would be twice as steep. If the rabbit ran in the
opposite
direction,
the magnitude
theAssessment
slope would be the same, but it would be negative.
Chapter
2 Practice
Problems,
Review,of
and
61. Test the following combinations and explain why each does not have the properties needed to describe the concept
of velocity: Δx + Δt, Δx − Δt, Δx × Δt, Δt/Δx.
SOLUTION: None of the combinations has the correct units, meters per second. In addition, Δx + Δt increases when
either term increases. The sign of Δx – Δt depends upon the relative sizes of Δx and Δt. Δx × Δt increases
when either increases. Δt/Δx decreases with increasing displacement and increases with increasing time
interval, which is backward from velocity.
62. Football When solving physics problems, what must be true about the motion of a football in order for you to treat
the football as if it were a particle?
SOLUTION: The football can be treated as a particle if its rotations are not important and if the distance it moves is
much larger than the football.
63. Figure 29 is a graph of two people running.
a. Describe the position of runner A relative to runner B at the y-intercept.
b. Which runner is faster?
c. What occurs at point P and beyond?
SOLUTION: a. Runner A has a head start by four units.
b. Runner B is faster, as shown by the steeper slope.
c. Runner B passes runner A at point P and is ahead of runner A beyond that point.
Chapter Assessment: Mixed Review
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64. Cycling A cyclist traveling along a straight path maintains a constant velocity of 5.0 m/s west. At time t = 0.0 s, the SOLUTION: a. Runner A has a head start by four units.
b. Runner B is faster, as shown by the steeper slope.
Chapter
2 Practice Problems, Review, and Assessment
c. Runner B passes runner A at point P and is ahead of runner A beyond that point.
Chapter Assessment: Mixed Review
64. Cycling A cyclist traveling along a straight path maintains a constant velocity of 5.0 m/s west. At time t = 0.0 s, the cyclist is 250 m west of point A. (Level 1)
a. Plot a position-time graph of the cyclist’s location from point A at 10.0-s intervals for a total time of 60.0 s.
b. What is the cyclist’s position from point A at 60.0 s?
c. What is the displacement from the starting position at 60.0 s?
SOLUTION: a.
b. c.
65. Figure 30 is a particle model diagram for a chicken casually walking across a road. Draw the corresponding
position-time graph, and write an equation to describe the chicken’s motion. (Level 1)
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SOLUTION: Page 29
c.
Chapter
2 Practice Problems, Review, and Assessment
65. Figure 30 is a particle model diagram for a chicken casually walking across a road. Draw the corresponding
position-time graph, and write an equation to describe the chicken’s motion. (Level 1)
SOLUTION: 66. Figure 31 shows position-time graphs for Joszi and Heike paddling canoes in a local river. (Level 1)
a. At what time(s) are Joszi and Heike in the same place? b. How long is Joszi paddling before passing Heike? c. Where on the river does it appear that there might be a swift current?
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SOLUTION: Page 30
Chapter 2 Practice Problems, Review, and Assessment
66. Figure 31 shows position-time graphs for Joszi and Heike paddling canoes in a local river. (Level 1)
a. At what time(s) are Joszi and Heike in the same place? b. How long is Joszi paddling before passing Heike? c. Where on the river does it appear that there might be a swift current?
SOLUTION: a. 1.0 h
b. 45 min
c. from 6.0 to 9.0 km from the origin
67. Driving Both car A and car B leave school when a stopwatch reads zero. Car A travels at a constant 75 km/h, and
car B travels at a constant 85 km/h. (Level 2)
a. Draw a position-time graph showing the motion of both cars over 3 hours. How far are the two cars from school when the stopwatch reads 2.0 h? Calculate the distances and show them on your graph. b. Both cars passed a gas station 120 km from the school. When did each car pass the gas station? Calculate the times and show them on your graph.
SOLUTION: a. eSolutions Manual - Powered by Cognero
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b. Both cars passed a gas station 120 km from the school. When did each car pass the gas station? Calculate the times and show them on your graph.
Chapter 2 Practice Problems, Review, and Assessment
SOLUTION: a. b.
a position-time graph for two cars traveling to a beach that is 50 km from school. At noon, Car A leaves a 68. Draw
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store that is 10 km closer to the beach than the school is and moves at 40 km/h. Car B starts from school at 12:30 p.m. and moves at 100 km/h. When does each car get to the beach? (Level 2)
Chapter
2 Practice Problems, Review, and Assessment
68. Draw a position-time graph for two cars traveling to a beach that is 50 km from school. At noon, Car A leaves a store that is 10 km closer to the beach than the school is and moves at 40 km/h. Car B starts from school at 12:30 p.m. and moves at 100 km/h. When does each car get to the beach? (Level 2)
SOLUTION: 69. Two cars travel along a straight road. When a stopwatch reads t = 0.00 h, car A is at xA = 48.0 km moving at a constant speed of 36.0 km/h. Later, when the watch reads t = 0.50 h, car B is at xB = 0.00 km moving at 48.0 km/h. Answer the following questions, first graphically by creating a position-time graph and then algebraically by writing
equations for the positions xA and xB as a function of the stopwatch time (t). (Level 3)
a. What will the watch read when car B passes car A?
b. At what position will car B pass car A?
c. When the cars pass, how long will it have been since car A was at the reference point?
SOLUTION: a.
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Chapter 2 Practice Problems, Review, and Assessment
a.
b. c. 70. The graph in Figure 32 depicts Jim’s movement along a straight path. The origin is at one end of the path. (Level 3)
a. Reverse Problem Write a story describing Jim’s movements along the path that would correspond to the motion
represented by the graph.
b. When is Jim 6.0 m from the origin?
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c. How much time passes between when Jim starts moving and when he is 12.0 m from the origin?
d. What is Jim’s average velocity between 37.0 s and 46.0 s?
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Chapter 2 Practice Problems, Review, and Assessment
70. The graph in Figure 32 depicts Jim’s movement along a straight path. The origin is at one end of the path. (Level 3)
a. Reverse Problem Write a story describing Jim’s movements along the path that would correspond to the motion
represented by the graph.
b. When is Jim 6.0 m from the origin?
c. How much time passes between when Jim starts moving and when he is 12.0 m from the origin?
d. What is Jim’s average velocity between 37.0 s and 46.0 s?
SOLUTION: a. Answers will vary, but a correct form of the answer is Jim walks 6 m in 7 s. He stops for 16 s. He
walks 6 m in 9 s and stops for 5 s. He turns around and walks back toward the origin. He walks 9 m in 9 s
and stops for 5 s. He then walks away from the origin again for 3 m in 1 s. He stops again for 5 s, and he
turns around and walks 6 m back toward the origin in 6 s.
b. from 7.0 to 23.0 s, momentarily at 43.0 s, and from 52.0 s to 57.0 s
c. Dt = 32.0 s - 0.0 s = 32.0 s
d. Chapter Assessment: Thinking Critically
71. Apply Calculators Members of a physics class stood 25 m apart and used stopwatches to measure the time at which a car traveling on the highway passed each person. Table 2 shows their data.
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Chapter
2 Practice Problems, Review, and Assessment
Chapter Assessment: Thinking Critically
71. Apply Calculators Members of a physics class stood 25 m apart and used stopwatches to measure the time at which a car traveling on the highway passed each person. Table 2 shows their data.
Use a graphing calculator to fit a line to a position-time graph of the data and to plot this line. Be sure to set the
display range of the graph so that all the data fit on it. Find the line’s slope. What was the car’s speed?
SOLUTION: The slope of the line and the speed of the car are about 19.7 m/s.
72. Apply Concepts You want to average 90 km/h on a car trip. You cover the first half of the distance at an average speed of 48 km/h. What average speed must you have for the second half of the trip to meet your goal? Is this reasonable? Note that the velocities are based on half the distance, not half the time.
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The slope of the line and the speed of the car are about 19.7 m/s.
Chapter
2 Practice Problems, Review, and Assessment
72. Apply Concepts You want to average 90 km/h on a car trip. You cover the first half of the distance at an average speed of 48 km/h. What average speed must you have for the second half of the trip to meet your goal? Is this reasonable? Note that the velocities are based on half the distance, not half the time.
SOLUTION: 73. Design an Experiment Every time someone drives a particular red motorcycle past your friend’s home, his father
becomes angry. He thinks the motorcycle is going too fast for the posted 25 mph (40 km/h) speed limit. Describe a simple experiment you could do to determine whether the motorcycle is speeding the next time it passes your friend’s
house.
SOLUTION: Possible answers: 1) Get several people together and give everyone a watch. Synchronize the watches
and stand along the street separated by a consistent distance, maybe 10 m or so. When the motorcycle
passes, have each person record the time (at least to an accuracy of seconds) that the motorcycle
crossed in front of the person. Plot a position-time graph, and compute the slope of the best-fit line. If the
slope is greater than 25 mph, the motorcycle is speeding. 2) Get someone with a driver’s license to drive
a car along the street at 25 mph in the same direction as you expect the motorcycle to go. If the distance
between the motorcycle and the car decreases, the motorcycle is speeding. If the distance between them
stays the same, the motorcycle is driving at the speed limit. If the distance increases, the motorcycle is
driving less than the speed limit.
74. Interpret Graphs Is it possible for an object’s position-time graph to be a horizontal line? A vertical line? If you
answer yes to either situation, describe the associated motion in words.
SOLUTION: It is possible to have a horizontal line as a position-time graph. This would indicate that the object’s
position is not changing, or in other words, that it is not moving. It is not possible to have a position-time
graph that is a vertical line, because this would mean the object is moving at an infinite speed.
Chapter Assessment: Writing in Physics
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8 75. Physicists have determined that the speed of light is 3.00×10 m/s. How did they arrive at this number? Read about
SOLUTION: It is possible to have a horizontal line as a position-time graph. This would indicate that the object’s
position is not changing, or in other words, that it is not moving. It is not possible to have a position-time
graph
that is a vertical
line,
becauseand
thisAssessment
would mean the object is moving at an infinite speed.
Chapter
2 Practice
Problems,
Review,
Chapter Assessment: Writing in Physics
8 75. Physicists have determined that the speed of light is 3.00×10 m/s. How did they arrive at this number? Read about
some of the series of experiments that scientists have performed to determine light’s speed. Describe how the
experimental techniques improved to make the experiments’ results more accurate.
SOLUTION: Answers will vary. Galileo attempted to determine the speed of light but was unsuccessful. Danish
astronomer Ole Roemer successfully measured the speed of light in 1676 by observing the moonrise of
one of Jupiter’s moons. His estimate was 140,000 miles/second (225,308 km/s). Many others since
have tried to measure it more accurately using rotating toothed wheels, rotating mirrors, and the Kerr
cell shutter.
76. Some species of animals have good endurance, while others have the ability to move very quickly, but for only a
short amount of time. Use reference sources to find two examples of each quality, and describe how it is helpful to
that animal.
SOLUTION: Answers will vary. Examples of animals that have high endurance to outlast predators or prey include
mules, bears, and coyotes. Animals that have the speed to quickly escape predators or capture prey
include cheetahs, antelopes, and deer.
Chapter Assessment: Cumulative Review
77. Convert each of the following time measurements to its equivalent in seconds.
a. 58 ns
b. 0.046 Gs
c. 9270 ms
d. 12.3 ks
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78. State the number of significant figures in the following measurements.
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SOLUTION: Answers will vary. Examples of animals that have high endurance to outlast predators or prey include
mules, bears, and coyotes. Animals that have the speed to quickly escape predators or capture prey
Chapter
2 Practice
Problems,
Review,
and Assessment
include
cheetahs,
antelopes,
and deer.
Chapter Assessment: Cumulative Review
77. Convert each of the following time measurements to its equivalent in seconds.
a. 58 ns
b. 0.046 Gs
c. 9270 ms
d. 12.3 ks
SOLUTION: 78. State the number of significant figures in the following measurements.
a. 3218 kg
b. 60.080 kg
c. 801 kg
d. 0.000534 kg
SOLUTION: a. 4
b. 5
c. 3
d. 3
79. Using a calculator, Chris obtained the following results. Rewrite each answer to each operation using the correct
number of significant figures.
a. 5.32 mm + 2.1 mm = 7.4200000 mm
b. 13.597 m × 3.65 m = 49.62905 m2
c. 83.2 kg –12.804 kg = 70.3960000 kg
SOLUTION: a. 7.4 mm
2
b. 49.6 m
c. 70.4 kg
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SOLUTION: a. 4
b. 5
Chapter
c. 3 2 Practice Problems, Review, and Assessment
d. 3
79. Using a calculator, Chris obtained the following results. Rewrite each answer to each operation using the correct
number of significant figures.
a. 5.32 mm + 2.1 mm = 7.4200000 mm
b. 13.597 m × 3.65 m = 49.62905 m2
c. 83.2 kg –12.804 kg = 70.3960000 kg
SOLUTION: a. 7.4 mm
2
b. 49.6 m
c. 70.4 kg
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