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TRANSCRIPT
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.
ANSWER: 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.
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).
ANSWER: Runner A passed the origin.
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. Atthat point the lines of the graph crossed, indicating that Runner B was beginning to be farther from the origin than Runner A.
ANSWER: Runner B
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.
ANSWER: at –50.0 m
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.
ANSWER: approximately 30 m
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
ANSWER:
a. 6.0 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
d. t = 1.8 h
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 x-direction (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.
ANSWER: a. 0.3 m/s b. 0.3 m/s north.
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?
ANSWER: a. 0.7 km/min b. = 0.7 km/min in the positive direction
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-m distance from in front of his house to the nearest stop sign.
SOLUTION:
ANSWER:
Chapter Assessment Section 4 How Fast: Mastering Concepts
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.
ANSWER: Both are straight lines that start at the same position, but the slope of the runner’s line is steeper.
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
ANSWER: 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.
ANSWER: 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.
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.
ANSWER: 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
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
ANSWER: 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, andcar 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.
b.
ANSWER:
b. t
a = 1.6 h, t
b = 1.4 h
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Chapter 2 Practice Problems, 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.
ANSWER: 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.
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).
ANSWER: Runner A passed the origin.
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. Atthat point the lines of the graph crossed, indicating that Runner B was beginning to be farther from the origin than Runner A.
ANSWER: Runner B
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.
ANSWER: at –50.0 m
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.
ANSWER: approximately 30 m
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
ANSWER:
a. 6.0 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
d. t = 1.8 h
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 x-direction (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.
ANSWER: a. 0.3 m/s b. 0.3 m/s north.
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?
ANSWER: a. 0.7 km/min b. = 0.7 km/min in the positive direction
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-m distance from in front of his house to the nearest stop sign.
SOLUTION:
ANSWER:
Chapter Assessment Section 4 How Fast: Mastering Concepts
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.
ANSWER: Both are straight lines that start at the same position, but the slope of the runner’s line is steeper.
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
ANSWER: 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.
ANSWER: 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.
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.
ANSWER: 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
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
ANSWER: 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, andcar 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.
b.
ANSWER:
b. t
a = 1.6 h, t
b = 1.4 h
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Chapter 2 Practice Problems, 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.
ANSWER: 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.
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).
ANSWER: Runner A passed the origin.
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. Atthat point the lines of the graph crossed, indicating that Runner B was beginning to be farther from the origin than Runner A.
ANSWER: Runner B
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.
ANSWER: at –50.0 m
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.
ANSWER: approximately 30 m
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
ANSWER:
a. 6.0 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
d. t = 1.8 h
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 x-direction (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.
ANSWER: a. 0.3 m/s b. 0.3 m/s north.
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?
ANSWER: a. 0.7 km/min b. = 0.7 km/min in the positive direction
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-m distance from in front of his house to the nearest stop sign.
SOLUTION:
ANSWER:
Chapter Assessment Section 4 How Fast: Mastering Concepts
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.
ANSWER: Both are straight lines that start at the same position, but the slope of the runner’s line is steeper.
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
ANSWER: 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.
ANSWER: 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.
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.
ANSWER: 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
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
ANSWER: 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, andcar 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.
b.
ANSWER:
b. t
a = 1.6 h, t
b = 1.4 h
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Chapter 2 Practice Problems, 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.
ANSWER: 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.
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).
ANSWER: Runner A passed the origin.
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. Atthat point the lines of the graph crossed, indicating that Runner B was beginning to be farther from the origin than Runner A.
ANSWER: Runner B
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.
ANSWER: at –50.0 m
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.
ANSWER: approximately 30 m
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
ANSWER:
a. 6.0 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
d. t = 1.8 h
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 x-direction (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.
ANSWER: a. 0.3 m/s b. 0.3 m/s north.
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?
ANSWER: a. 0.7 km/min b. = 0.7 km/min in the positive direction
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-m distance from in front of his house to the nearest stop sign.
SOLUTION:
ANSWER:
Chapter Assessment Section 4 How Fast: Mastering Concepts
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.
ANSWER: Both are straight lines that start at the same position, but the slope of the runner’s line is steeper.
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
ANSWER: 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.
ANSWER: 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.
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.
ANSWER: 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
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
ANSWER: 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, andcar 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.
b.
ANSWER:
b. t
a = 1.6 h, t
b = 1.4 h
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Chapter 2 Practice Problems, 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.
ANSWER: 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.
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).
ANSWER: Runner A passed the origin.
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. Atthat point the lines of the graph crossed, indicating that Runner B was beginning to be farther from the origin than Runner A.
ANSWER: Runner B
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.
ANSWER: at –50.0 m
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.
ANSWER: approximately 30 m
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
ANSWER:
a. 6.0 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
d. t = 1.8 h
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 x-direction (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.
ANSWER: a. 0.3 m/s b. 0.3 m/s north.
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?
ANSWER: a. 0.7 km/min b. = 0.7 km/min in the positive direction
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-m distance from in front of his house to the nearest stop sign.
SOLUTION:
ANSWER:
Chapter Assessment Section 4 How Fast: Mastering Concepts
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.
ANSWER: Both are straight lines that start at the same position, but the slope of the runner’s line is steeper.
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
ANSWER: 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.
ANSWER: 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.
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.
ANSWER: 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
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
ANSWER: 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, andcar 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.
b.
ANSWER:
b. t
a = 1.6 h, t
b = 1.4 h
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Chapter 2 Practice Problems, 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.
ANSWER: 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.
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).
ANSWER: Runner A passed the origin.
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. Atthat point the lines of the graph crossed, indicating that Runner B was beginning to be farther from the origin than Runner A.
ANSWER: Runner B
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.
ANSWER: at –50.0 m
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.
ANSWER: approximately 30 m
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
ANSWER:
a. 6.0 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
d. t = 1.8 h
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 x-direction (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.
ANSWER: a. 0.3 m/s b. 0.3 m/s north.
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?
ANSWER: a. 0.7 km/min b. = 0.7 km/min in the positive direction
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-m distance from in front of his house to the nearest stop sign.
SOLUTION:
ANSWER:
Chapter Assessment Section 4 How Fast: Mastering Concepts
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.
ANSWER: Both are straight lines that start at the same position, but the slope of the runner’s line is steeper.
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
ANSWER: 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.
ANSWER: 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.
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.
ANSWER: 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
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
ANSWER: 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, andcar 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.
b.
ANSWER:
b. t
a = 1.6 h, t
b = 1.4 h
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Chapter 2 Practice Problems, 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.
ANSWER: 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.
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).
ANSWER: Runner A passed the origin.
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. Atthat point the lines of the graph crossed, indicating that Runner B was beginning to be farther from the origin than Runner A.
ANSWER: Runner B
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.
ANSWER: at –50.0 m
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.
ANSWER: approximately 30 m
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
ANSWER:
a. 6.0 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
d. t = 1.8 h
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 x-direction (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.
ANSWER: a. 0.3 m/s b. 0.3 m/s north.
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?
ANSWER: a. 0.7 km/min b. = 0.7 km/min in the positive direction
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-m distance from in front of his house to the nearest stop sign.
SOLUTION:
ANSWER:
Chapter Assessment Section 4 How Fast: Mastering Concepts
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.
ANSWER: Both are straight lines that start at the same position, but the slope of the runner’s line is steeper.
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
ANSWER: 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.
ANSWER: 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.
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.
ANSWER: 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
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
ANSWER: 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, andcar 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.
b.
ANSWER:
b. t
a = 1.6 h, t
b = 1.4 h
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Chapter 2 Practice Problems, 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.
ANSWER: 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.
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).
ANSWER: Runner A passed the origin.
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. Atthat point the lines of the graph crossed, indicating that Runner B was beginning to be farther from the origin than Runner A.
ANSWER: Runner B
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.
ANSWER: at –50.0 m
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.
ANSWER: approximately 30 m
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
ANSWER:
a. 6.0 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
d. t = 1.8 h
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 x-direction (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.
ANSWER: a. 0.3 m/s b. 0.3 m/s north.
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?
ANSWER: a. 0.7 km/min b. = 0.7 km/min in the positive direction
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-m distance from in front of his house to the nearest stop sign.
SOLUTION:
ANSWER:
Chapter Assessment Section 4 How Fast: Mastering Concepts
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.
ANSWER: Both are straight lines that start at the same position, but the slope of the runner’s line is steeper.
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
ANSWER: 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.
ANSWER: 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.
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.
ANSWER: 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
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
ANSWER: 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, andcar 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.
b.
ANSWER:
b. t
a = 1.6 h, t
b = 1.4 h
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Chapter 2 Practice Problems, 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.
ANSWER: 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.
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).
ANSWER: Runner A passed the origin.
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. Atthat point the lines of the graph crossed, indicating that Runner B was beginning to be farther from the origin than Runner A.
ANSWER: Runner B
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.
ANSWER: at –50.0 m
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.
ANSWER: approximately 30 m
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
ANSWER:
a. 6.0 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
d. t = 1.8 h
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 x-direction (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.
ANSWER: a. 0.3 m/s b. 0.3 m/s north.
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?
ANSWER: a. 0.7 km/min b. = 0.7 km/min in the positive direction
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-m distance from in front of his house to the nearest stop sign.
SOLUTION:
ANSWER:
Chapter Assessment Section 4 How Fast: Mastering Concepts
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.
ANSWER: Both are straight lines that start at the same position, but the slope of the runner’s line is steeper.
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
ANSWER: 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.
ANSWER: 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.
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.
ANSWER: 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
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
ANSWER: 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, andcar 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.
b.
ANSWER:
b. t
a = 1.6 h, t
b = 1.4 h
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Chapter 2 Practice Problems, 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.
ANSWER: 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.
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).
ANSWER: Runner A passed the origin.
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. Atthat point the lines of the graph crossed, indicating that Runner B was beginning to be farther from the origin than Runner A.
ANSWER: Runner B
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.
ANSWER: at –50.0 m
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.
ANSWER: approximately 30 m
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
ANSWER:
a. 6.0 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
d. t = 1.8 h
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 x-direction (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.
ANSWER: a. 0.3 m/s b. 0.3 m/s north.
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?
ANSWER: a. 0.7 km/min b. = 0.7 km/min in the positive direction
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-m distance from in front of his house to the nearest stop sign.
SOLUTION:
ANSWER:
Chapter Assessment Section 4 How Fast: Mastering Concepts
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.
ANSWER: Both are straight lines that start at the same position, but the slope of the runner’s line is steeper.
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
ANSWER: 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.
ANSWER: 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.
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.
ANSWER: 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
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
ANSWER: 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, andcar 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.
b.
ANSWER:
b. t
a = 1.6 h, t
b = 1.4 h
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Chapter 2 Practice Problems, 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.
ANSWER: 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.
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).
ANSWER: Runner A passed the origin.
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. Atthat point the lines of the graph crossed, indicating that Runner B was beginning to be farther from the origin than Runner A.
ANSWER: Runner B
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.
ANSWER: at –50.0 m
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.
ANSWER: approximately 30 m
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
ANSWER:
a. 6.0 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
d. t = 1.8 h
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 x-direction (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.
ANSWER: a. 0.3 m/s b. 0.3 m/s north.
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?
ANSWER: a. 0.7 km/min b. = 0.7 km/min in the positive direction
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-m distance from in front of his house to the nearest stop sign.
SOLUTION:
ANSWER:
Chapter Assessment Section 4 How Fast: Mastering Concepts
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.
ANSWER: Both are straight lines that start at the same position, but the slope of the runner’s line is steeper.
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
ANSWER: 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.
ANSWER: 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.
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.
ANSWER: 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
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
ANSWER: 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, andcar 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.
b.
ANSWER:
b. t
a = 1.6 h, t
b = 1.4 h
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Chapter 2 Practice Problems, 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.
ANSWER: 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.
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).
ANSWER: Runner A passed the origin.
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. Atthat point the lines of the graph crossed, indicating that Runner B was beginning to be farther from the origin than Runner A.
ANSWER: Runner B
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.
ANSWER: at –50.0 m
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.
ANSWER: approximately 30 m
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
ANSWER:
a. 6.0 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
d. t = 1.8 h
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 x-direction (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.
ANSWER: a. 0.3 m/s b. 0.3 m/s north.
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?
ANSWER: a. 0.7 km/min b. = 0.7 km/min in the positive direction
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-m distance from in front of his house to the nearest stop sign.
SOLUTION:
ANSWER:
Chapter Assessment Section 4 How Fast: Mastering Concepts
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.
ANSWER: Both are straight lines that start at the same position, but the slope of the runner’s line is steeper.
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
ANSWER: 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.
ANSWER: 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.
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.
ANSWER: 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
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
ANSWER: 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, andcar 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.
b.
ANSWER:
b. t
a = 1.6 h, t
b = 1.4 h
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Chapter 2 Practice Problems, 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.
ANSWER: 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.
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).
ANSWER: Runner A passed the origin.
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. Atthat point the lines of the graph crossed, indicating that Runner B was beginning to be farther from the origin than Runner A.
ANSWER: Runner B
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.
ANSWER: at –50.0 m
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.
ANSWER: approximately 30 m
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
ANSWER:
a. 6.0 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
d. t = 1.8 h
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 x-direction (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.
ANSWER: a. 0.3 m/s b. 0.3 m/s north.
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?
ANSWER: a. 0.7 km/min b. = 0.7 km/min in the positive direction
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-m distance from in front of his house to the nearest stop sign.
SOLUTION:
ANSWER:
Chapter Assessment Section 4 How Fast: Mastering Concepts
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.
ANSWER: Both are straight lines that start at the same position, but the slope of the runner’s line is steeper.
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
ANSWER: 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.
ANSWER: 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.
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.
ANSWER: 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
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
ANSWER: 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, andcar 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.
b.
ANSWER:
b. t
a = 1.6 h, t
b = 1.4 h
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Chapter 2 Practice Problems, Review, and Assessment