# 8. As a cart travels around a horizontal circular track, the cart must undergo a change in (1) velocity (3) speed (2) inertia (4) weight

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1 1. What is the average speed of an object that travels 6.00 meters north in 2.00 seconds and then travels 3.00 meters east in 1.00 second? 9.00 m/s 3.00 m/s m/s 4.24 m/s 2. What is the distance traveled by an object that moves with an average speed of 6.0 meters per second for 8.0 seconds? 0.75 m 14 m 1.3 m 48 m 3. A cart starting from rest travels a distance of 3.6 meters in 1.8 seconds. The average speed of the cart is 0.20 m/s 0.50 m/s 2.0 m/s 5.0 m/s 4. A car travels 20. meters east in 1.0 second. The displacement of the car at the end of this 1.0-second interval is 20. m 20. m east 20. m/s 20. m/s east 5. A baseball pitcher throws a fastball at 42 meters per second. If the batter is 18 meters from the pitcher, approximately how much time does it take for the ball to reach the batter? 1.9 s 0.86 s 2.3 s 0.43 s 6. The average speed of a plane was 600 kilometers per hour. How long did it take the plane to travel 120 kilometers? 0.2 hour 0.7 hour 0.5 hour 5 hours 7. What is the average velocity of a car that travels 30. kilometers due west in 0.50 hour? 15 km/hr 15 km/hr west 60. km/hr 60. km/hr west 8. As a cart travels around a horizontal circular track, the cart must undergo a change in velocity speed inertia weight 9. Two cars, A and B, are 400. meters apart. Car A travels due east at 30. meters per second on a collision course with car B, which travels due west at 20. meters per second. How much time elapses before the two cars collide? 8.0 s 20. s 13 s 40. s 10. A group of bike riders took a 4.0-hour trip. During the first 3.0 hours, they traveled a total of 50. kilometers, but during the last hour they traveled only 10. kilometers. What was the group s average speed for the entire trip? 15 km/hr 40. km/hr 30. km/hr 60. km/hr 11. A car travels 90. meters due north in 15 seconds. Then the car turns around and travels 40. meters due south in 5.0 seconds. What is the magnitude of the average velocity of the car during this 20.-second interval? 2.5 m/s 6.5 m/s 5.0 m/s 7.0 m/s 12. One car travels 40. meters due east in 5.0 seconds, and a second car travels 64 meters due west in 8.0 seconds. During their periods of travel, the cars definitely had the same average velocity change in momentum total displacement average speed 13. In a 4.0-kilometer race, a runner completes the first kilometer in 5.9 minutes, the second kilometer in 6.2 minutes, the third kilometer in 6.3 minutes, and the final kilometer in 6.0 minutes. The average speed of the runner for the race is approximately 0.16 km/min 12 km/min 0.33 km/min 24 km/min 14. A car moving at a speed of 8.0 meters per second enters a highway and accelerates at 3.0 meters per second 2. How fast will the car be moving after it has accelerated for 56 meters? 24 m/s 18 m/s 20. m/s 4.0 m/s

2 15. A jogger accelerates at a constant rate as she travels 5.0 meters along a straight track from point A to point B,as shown in the diagram below. 20. A boat initially traveling at 10. meters per second accelerates uniformly at the rate of 5.0 meters per second 2 for 10. seconds. How far does the boat travel during this time? 50. m 350 m 250 m 500 m 21. A roller coaster, traveling with an initial speed of 15 meters per second, decelerates uniformly at 7.0 meters per second 2 to a full stop. Approximately how far does the roller coaster travel during its deceleration? 1.0 m 16 m 2.0 m 32 m If her speed was 2.0 meters per second at point A and will be 3.0 meters per second at point B, how long will it take her to go from A to B? 1.0 s 3.3 s 2.0 s 4.2 s 16. Base your answer to the following question on the information below. A 1,000-kilogram car traveling with a velocity of +20. meters per second decelerates uniformly at 5.0 meters per second 2 until it comes to rest. What is the total distance the car travels as it decelerates to rest? 10. m 40. m 20. m 80. m 17. A race car traveling at 10. meters per second accelerates at 1.5 meters per seconds 2 while traveling a distance of 600. meters. The final speed of the race car is approximately 1900 m/s 910 m/s 150 m/s 44 m/s 18. A car accelerates uniformly from rest at 3.2 m/s 2. When the car has traveled a distance of 40. meters, its speed will be 8.0 m/s 16 m/s 12.5 m/s 128 m/s 19. A car initially traveling at a speed of 16 meters per second accelerates uniformly to a speed of 20. meters per second over a distance of 36 meters. What is the magnitude of the car s acceleration? 0.11 m/s m/s m/s m/s A rocket initially at rest on the ground lifts off vertically with a constant acceleration of meters per second 2. How long will it take the rocket to reach an altitude of meters? s s s s 23. A car is accelerated at 4.0 m/s 2 from rest. The car will reach a speed of 28 meters per second at the end of 3.5 sec 14 sec 7.0 sec 24 sec 24. An object starting from rest accelerates at a rate of 3.0 meters/second squared for 6.0 seconds. The velocity of the object at the end of this time is 0.50 m/s 3.0 m/s 2.0 m/s 18 m/s 25. An object has a constant acceleration of 2.0 meters per second 2. The time required for the object to accelerate from 8.0 meters per second to 28 meters per second is 20. s 10. s 16. s 4.0 s 26. A child riding a bicycle at 15 meters per second decelerates at the rate of 3.0 meters per second 2 for 4.0 seconds. What is the child's speed at the end of the 4.0 seconds? 12 m/s 3.0 m/s 27 m/s 7.0 m/s 27. A locomotive starts from rest and accelerates at 0.12 meter per second 2 to a speed of 2.4 meters per second in 20. seconds. This motion could best be described as constant acceleration and constant velocity increasing acceleration and constant velocity constant acceleration and increasing velocity increasing acceleration and increasing velocity

3 28. A bicyclist accelerates from rest to a speed of 5.0 meters per second in 10. seconds. During the same 10. seconds, a car accelerates from a speed of 22 meters per second to a speed of 27 meters per second. Compared to the acceleration of the bicycle, the acceleration of the car is less the same greater 29. A car having an initial velocity of 12 meters per second east slows uniformly to 2 meters per second east in 4.0 seconds. The acceleration of the car during this 4.0-second interval is 2.5 m/s 2 west 6.0 m/s 2 west 2.5 m/s 2 east 6.0 m/s 2 east 30. A ball dropped from rest falls freely until it hits the ground with a speed of 20 meters per second. The time during which the ball is in free fall is approximately 1 s 0.5 s 2 s 10 s 35. As a body falls freely near the surface of the Earth, its acceleration decreases remains the same increases 36. An object, initially at rest, falls freely near the Earth's surface. How long does it take the object to attain a speed of 98 meters per second? 0.1 sec 98 sec 10 sec 960 sec Base your answers to questions 37 and 38 on the graphs below which represent various phenomena in physics. [Note: A graph may be used more than once.] 31. An observer recorded the data above for the motion of a car undergoing constant acceleration. 37. Which graph best represents the relationship between speed and time for an object in free fall near the Earth's surface? A C B D What was the magnitude of the acceleration of the car? 1.3 m/s m/s m/s m/s Two unequal masses falling freely from the same point above the earth's surface would experience the same acceleration decrease in potential energy increase in kinetic energy increase in momentum 33. If the mass of an object were doubled, its acceleration due to gravity would be halved unchanged doubled quadrupled 38. Which graph best represents the relationship between velocity and time for an object thrown vertically upward near the surface of the Earth? A C B D 39. Which graph best represents the motion of a freely falling body near the Earth's surface? 34. As an object falls freely near the surface of the Earth, its velocity decreases remains the same increases

4 40. As shown in the diagram below, an astronaut on the Moon is holding a baseball and a balloon. The astronaut releases both objects at the same time. 43. Base your answer to the following question on the diagram below which shows a 1-kilogram mass and a 2-kilogram mass being dropped from a building 100 meters high. What does the astronaut observe? [Note: The Moon has no atmosphere.] The baseball falls slower than the balloon. The baseball falls faster than the balloon. The baseball and balloon fall at the same rate. The baseball and balloon remain suspended and do not fall. 41. An object starts from rest and falls freely. What is the velocity of the object at the end of 3.00 seconds? 9.81 m/s 29.4 m/s 19.6 m/s 88.2 m/s 42. An object dropped from rest will have a velocity of approximately 30. meters per second at the end of 1.0 s 3.0 s 2.0 s 4.0 s Halfway down, the acceleration is greater for the 1-kilogram mass greater for the 2-kilogram mass the same for both masses 44. Objects A and B are dropped from rest near Earth s surface. Object A has mass m and object B has mass 2m. After 2 seconds of free fall, object A has a speed v and has fallen a distance d. What are the speed and distance of fall of object B after 2 seconds of free fall? speed = v/2; distance = d/2 speed = v; distance = d speed = v/2; distance = 2d speed = 2v; distance = 2d 45. A 4.0-kilogram rock and a 1.0-kilogram stone fall freely from rest from a height of 100 meters. After they fall for 2.0 seconds, the ratio of the rock s speed to the stone s speed is 1:1 2:1 1:2 4:1 46. An object is dropped from rest and falls freely 20. meters to Earth. When is the speed of the object 9.8 meters per second? during the entire first second of its fall at the end of its first second of fall during its entire time of fall after it has fallen 9.8 meters

5 47. Which graph best represents the relationship between the acceleration of an object falling freely near the surface of Earth and the time that it falls? 48. A softball is thrown straight up, reaching a maximum height of 20 meters. Neglecting air resistance, what is the ball's approximate vertical speed when it hits the ground? 10 m/sec 15 m/sec 20 m/sec 40 m/sec 49. A rock falls freely from rest near the surface of a planet where the acceleration due to gravity is 4.0 meters per second 2. What is the speed of this rock after it falls 32 meters? 8.0 m/s 25 m/s 16 m/s 32 m/s 50. An object falls freely from rest near the surface of Earth. What is the speed of the object after having fallen a distance at 4.90 meters? 4.90 m/s 24.0 m/s 9.80 m/s 96.1 m/s 51. A rock falls from rest off a high cliff. How far has the rock fallen when its speed is 39.2 meters per second? [Neglect friction.] 19.6 m 78.3 m 44.1 m 123 m 52. An object is allowed to fall freely near the surface of a planet. The object has an acceleration due to gravity of 24 m/s 2. How far will the object fall during the first second? 24 meters 9.8 meters 12 meters 4.9 meters 53. Starting from rest, object A falls freely for 2.0 seconds, and object B falls freely for 4.0 seconds. Compared with object A, object B falls one-half as far three times as far twice as far four times as far 54. An object is allowed to fall freely near the surface of a planet. The object falls 54 meters in the first 3.0 seconds after it is released. The acceleration due to gravity on that planet is 6.0 m/s 2 27 m/s 2 12 m/s m/s A stone is dropped from a bridge 45 meters above the surface of a river. Approximately how many seconds does the stone take to reach the water's surface? 1.0 s 3.0 s 10. s 22 s 56. In an experiment that measures how fast a student reacts, a meter stick dropped from rest falls 0.20 meter before the student catches it. The reaction time of the student is approximately 0.10 s 0.30 s 0.20 s 0.40 s 57. A ball is thrown straight up with a speed of 12 meters per second near the surface of Earth. What is the maximum height reached by the ball? [Neglect air friction.] 15 m 1.2 m 7.3 m 0.37 m 58. The graph at the right represents the relationship between distance and time for an object in motion. During which interval is the speed of the object changing? AB CD BC DE

6 59. The graph below represents the relationship between distance and time for an object. 62. The graph at the right represents the motion of a body that is moving with increasing acceleration increasing speed decreasing acceleration constant speed What is the instantaneous speed of the object at t = 5.0 seconds? 0 m/s 5.0 m/s 2.0 m/s 4.0 m/s Base your answers to questions 63 through 67 on the graph below which represents the displacement of an object as a function of time. 60. The displacement-time graph below represents the motion of a cart along a straight line. 63. How far is the object from the starting point at the end of 3 seconds? 0 m 3.0 m 2.0 m 9.0 m During which interval was the cart accelerating? AB CD BC DE 61. The graph at the right represents the relationship between distance and time for an object moving in a straight line. According to the graph, the object is motionless moving at a constant speed decelerating accelerating 64. What is the velocity of the object at t = 1 second? 1.0 m/s 3.0 m/s 2.0 m/s 1.5 m/s 65. During which time interval is the object at rest? 0-2 s 3-4 s 2-3 s 4-6 s 66. What is the average velocity of the object from t = 0 to t = 3 seconds? 1.0 m/s 3.0 m/s 2.0 m/s 0 m/s 67. During which time interval is the object accelerating? 0-2 s 3-4 s 2-3 s 4-6 s

7 68. Which two graphs best represent the motion of an object falling freely from rest near Earth's surface? 71. The uniform motion of a cart is shown in the distance versus time graph below. What is the average speed of the cart? 0.5 m/s 5 m/s 2 m/s 50 m/s 72. Base your answer to the following question on the diagram below which shows a 1-kilogram stone being dropped from a bridge 100 meters above a gorge. 69. The distance-time graph at the right represents the motion of a laboratory cart. According to this graph, the cart is slowing down speeding up not moving moving at a constant speed 70. The graph at the right represents the motion of a cart. According to the graph, as time increases, the speed of the cart Which graph of distance traveled versus time represents the motion of the freely falling stone? decreases remains the same increases

8 Base your answers to questions 73 and 74 on the graph below, which represents the relationship between the displacement of an object and its time of travel along a straight line. 76. Which graph best represents the motion of an object whose speed is increasing? 73. What is the average speed of the object during the first 4.0 seconds? 0 m/s 8 m/s 2 m/s 4 m/s 77. Which graph best represents the relationship between acceleration due to gravity and mass for objects near the surface of Earth? [Neglect air resistance.] 74. What is the magnitude of the object's total displacement after 8.0 seconds? 0 m 8 m 2 m 16 m 75. Which pair of graphs represent the same motion?

9 78. Which graph best represents the motion of a block accelerating uniformly down an inclined plane?

10 79. Which pair of graphs represents the same motion of an object? 80. The graph below shows the speed of an object plotted against the time. Base your answers to questions 81 through 83 on Cars A and B both start from rest at the same location at the same time. The total distance traveled by the object during the first 4 seconds is 0.5 meter 8 meters 2 meters 4 meters 81. Compared to the total distance traveled by car B during the 10 seconds, the total distance traveled by car A is less the same greater 82. What is the magnitude of the acceleration of car A during the period between t = 8 seconds and t = 10 seconds? 20 m/s 2 8 m/s 2 16 m/s 2 4 m/s Compared to the speed of car B at 6 seconds, the speed of car A at 6 seconds is less the same greater

11 Base your answers to questions 84 through 88 on the graph below, which represents the motion of cars A and B on a straight track. Car B passes car A at the same instant that car A starts from rest at t = 0 seconds. 88. What is the acceleration of car A during the interval between t = 0 and t = 60? 1 m./sec./sec. 20 m./sec./sec. 10 m./sec./sec. 30 m./sec./sec. Base your answers to questions 89 through 93 on the accompanying graph which represents the motions of four cars on a straight road. 84. How far did car A travel in the interval between t = 0 and t = 60? 30 m. 1,800 m. 360 m. 3,600 m. 85. How long after t = 0 did it take car A to catch up to car B? 10 sec. 30 sec. 20 sec. 60 sec. 86. During the time intervals given below, which car traveled the greatest distance? car A from t = 0 to t = 30 car A from t = 30 to t = 60 car B from t = 0 to t = 30 car B from t = 30 to t = Which car moves the greatest distance in time interval t = 10 seconds to t = 16 seconds? A C B D 90. Which graph best represents the relationship between distance and time for car C? 87. Which distance-time graph best represents the motion of car B during the time interval between t = 0 and t = 60? 91. Which car has zero acceleration? A C B D 92. Which car is decelerating? A C B D 93. The speed of car C at t = 20 seconds is closest to 60 m/sec 3.0 m/sec 45 m/sec 600 m/sec

12 Base your answers to questions 94 through 99 on the graph below which represents the relationship between speed and time for an object in motion along a straight line. Base your answers to questions 100 through 102 on the graph below which represents the relationship between velocity and time for a 2.0-kilogram cart that is initially at rest and starts moving northward. 94. What is the total distance traveled by the object during the first 3 seconds? 15 m 25 m 20 m 30 m 95. What is the acceleration of the object during the time interval t = 3 seconds to t = 5 seconds? 5.0 m/sec m/sec m/sec m/sec During which interval is the object's acceleration the greatest? AB DE CD EF 97. What is the average speed of the object during the time interval t = 6 seconds to t = 8 seconds'? 7.5 m/sec 15 m/sec 10 m/sec 17.5 m/sec 100. At which value of t will the cart be back at the starting point? t = 2.5 s t = 3 s t = 8.5 s t = 5 s 101. What is the acceleration of the cart at t = 8 seconds? 0 m/s 2 20 m/s 2 10 m/s 2-20 m/s In which direction is the cart traveling at t = 4 seconds? north south east west Base your answers to questions 103 and 104 on the graph below, which shows the velocity of a 1,500-kilogram car during a 20- second-time interval. 98. During the interval t = 8 seconds to t = 10 seconds, the speed of the object is zero decreasing increasing constant, but not zero 99. What is the maximum speed reached by the object during the 10 seconds of travel? 10 m/sec 150 m/sec 25 m/sec 250 m/sec 103. The acceleration of the car during time interval AB is 0.40 m./sec m./sec m./sec m./sec. 2

13 104. During time interval CD, the average velocity of the car is 7.5 m./sec. 15 m./sec m./sec. 35 m./sec The speed-time graph shown on the right represents the motion of an object Which graph best represents the relationship between velocity and time for an object which accelerates uniformly for 2 seconds, then moves at a constant velocity for 1 second, and finally decelerates for 3 seconds? Which graph best represents the relationship between acceleration and time for this object? 107. The graph at the right shows the relationship between speed and time for two objects, A and B. Compared with the acceleration of object B, the acceleration of object A is one-third as great three times as great twice as great the same

14 108. The graph below shows speed as a function of time for four cars A, B, C, and D, in straight-line motion. Which car experienced the greatest average acceleration during this 6.0-second interval? car A car C car B car D 109. The diagram below represents the relationship between velocity and time of travel for four cars, A, B, C, and D, in straight-line motion. Which car has the greatest acceleration during the time interval 10. seconds to 15 seconds? A C B D

15 Base your answers to questions 110 through 112 on the information and data table below. A car is traveling due north at 24.0 meters per second when the driver sees an obstruction on the highway. The data table below shows the velocity of the car at 1.0-second intervals as it is brought to rest on the straight, level highway Using the information in the data table, construct a graph on the grid using the data points for velocity versus time Draw the best-fit line Using your graph, determine the acceleration of the car. [Show all calculations, including the equation and substitution with units.]

16 Base your answers to questions 113 through 116 on the data table below, which describes the motion of an object moving in a straight line Plot the data points Draw the line of best-fit On the same grid, sketch a line representing an object decelerating uniformly in a straight line Based on your line of best-fit, what is the acceleration of the object? Base your answers to questions 117 and 118 on the information below. A hiker walks 5.00 kilometers due north and then 7.00 kilometers due east What is the magnitude of her resultant displacement? 118. What total distance has she traveled?

17 119. Two physics students have been selected by NASA to accompany astronauts on a future mission to the Moon. The students are to design and carryout a simple experiment to measure the acceleration due to gravity on the surface of the Moon. Describe an experiment that the students could conduct to measure the acceleration due to gravity on the Moon. Your description must include: the equipment needed what quantities would be measured using the equipment what procedure the students should follow inconducting their experiment what equations and/or calculations the students would need to do to arrive at a value for the acceleration due to gravity on the Moon Base your answers to questions 120 and 121 on the information below. A physics class is to design an experiment to determine the acceleration of a student on inline skates coasting straight down a gentle incline. The incline has a constant slope. The students have tape measures, traffic cones, and stopwatches Describe a procedure to obtain the measurements necessary for this experiment Indicate which equation(s) they should use to determine the student s acceleration. Base your answers to questions 122 and 123 on the information below. A car traveling at a speed of 13 meters per second accelerates uniformly to a speed of 25 meters per second in 5.0 seconds Calculate the magnitude of the acceleration of the car during this 5.0-second time interval. [Show all work, including the equation and substitution with units.] 123. A truck traveling at a constant speed covers the same total distance as the car in the same 5.0-second time interval. Determine the speed of the truck.

18 Base your answers to questions 124 through 126 on the information below. A car on a straight road starts from rest and accelerates at 1.0 meter per second 2 for 10. seconds. Then the car continues to travel at constant speed for an additional 20. seconds Determine the speed of the car at the end of the first 10. seconds On the grid provided, use a ruler or straightedge to construct a graph of the car's speed as a function of time for the entire 30.-second interval Calculate the distance the car travels in the first 10. seconds. [Show all work, including the equation and substitution with units.]

19 Answer Key Wala_velocity_acceleratio_freefall [Oct 15, 2010]

20 Answer Key Wala_velocity_acceleratio_freefall [Oct 15, 2010] Graph 111. The best fit line must be straight m/s 2 south 113. Credit for plotting data correctly

21 Answer Key Wala_velocity_acceleratio_freefall [Oct 15, 2010] 115. Credit for drawing a decelerating straight line Credit for indicating that the acceleration of the object is 1.2 m/s 2 or an answer that is consistent with the student's graph km or 8.6 km km or 12. km or 12 km 119. freefall object, meterstick, stopwatch time of fall, distance of fall drop object from measured height, time its fall d = v i t at2 pendulum string, mass, stopwatch, meterstick length of pendulum, period measure length of pendulum, period of pendulum T = 2p ( g ) spring scale spring scale, known mass weight on Moon of known mass hang the weight on the spring scale and weigh it F g(m) = mg M 120. Examples: setting up a measured distance. measuring the time to travel that distance d = v i t + at m/s m/s d = v i t + ½at 2 d = 0 + ½(1.0 m/s 2 )(10. s) 2 d = 50. m or d = area = ½bh d = ½(10. s)( 10. m/s) d = 50. m

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