Regents Exam Practice: Measurement, Kinematics, Free Fall, PJM, and UCM 1. Which quantity and unit are correctly paired? 2. Which is a derived unit? meter second kilogram Newton 3. The fundamental unit of mass in the mks system is the milligram gram kilogram decigram 4. The diameter of a United States penny is closest to 10 0 m 10 1 m 10 2 m 10 3 m 5. The length of a dollar bill is approximately 1.5 10 2 m 1.5 10 1 m 1.5 10 1 m 1.5 10 2 m 6. The mass of a high school football player is approximately 10 0 kg 10 1 kg 10 2 kg 10 3 kg 7. Which object weighs approximately 1 Newton? dime paper clip physics student golf ball 8. The area of a page in a test booklet is closest to 0.6 cm 2 6 cm 2 60 cm 2 600 cm 2 9. A baseball player runs 27.4 meters from the batter's box to first base, overruns first base by 3.0 meters, and then returns to first base. Compared to the total distance traveled by the player, the magnitude of the player's total displacement from the batter's box is 3.0 m shorter 6.0 m shorter 3.0 m longer 6.0 m longer 10. A student on an amusement park ride moves in a circular path with a radius of 3.5 meters once every 8.9 seconds. The student moves at an average speed of 0.39 m/s 1.2 m/s 2.5 m/s 4.3 m/s 11. Which graph best represents the motion of a block accelerating uniformly down an inclined plane?
12. Which pair of graphs represent the same motion? 13. Which two graphs best represent the motion of an object falling freely from rest near Earth's surface? 15. 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 20 m/sec 15 m/sec 40 m/sec 16. An astronaut standing on a platform on the Moon drops a hammer. If the hammer falls 6.0 meters vertically in 2.7 seconds, what is its acceleration? 1.6 m/s 2 2.2 m/s 2 4.4 m/s 2 9.8 m/s 2 17. A student throws a baseball vertically upward and then catches it. If vertically upward is considered to be the positive direction, which graph best represents the relationship between velocity and time for the baseball? [Neglect friction.] 14. 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 1:2 2:1 4:1 18. A skier starting from rest skis straight down a slope 50. meters long in 5.0 seconds. What is the magnitude of the acceleration of the skier? 20. m/s 2 9.8 m/s 2 5.0 m/s 2 4.0 m/s 2
19. A car, initially traveling east with a speed of 5.0 meters per second, is accelerated uniformly at 2.0 meters per second 2 east for 10. seconds along a straight line. During this 10.-second interval the car travels a total distance of 50. m 60. m 1.0 10 2 m 1.5 10 2 m 20. A rocket initially at rest on the ground lifts off vertically with a constant acceleration of 2.0 10 1 meters per second 2. How long will it take the rocket to reach an altitude of 9.0 10 3 meters? 3.0 10 1 s 4.3 10 1 s 4.5 10 2 s 9.0 10 2 s 21. A child riding a bicycle at 15 meters per second accelerates at -3.0 meters per second 2 for 4.0 seconds. What is the child s speed at the end of this 4.0-second interval? 12 m/s 27 m/s 3.0 m/s 7.0 m/s 22. 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?
23. Which graph best represents an object in equilibrium moving in a straight line? 24. Cars A and B both start from rest at the same location at the same time. Compared to the speed of car B at 6 seconds, the speed of car A at 6 seconds is less greater the same
25. Base your answer to the following question on the graph below which represents the relationship between speed and time for an object in motion along a straight line. During what time period was the car decelerating as it was moving right 0 to 1 s and 3 s to 4 s 1 s to 3 s and 5 s to 6 s 6 s to 10 s None of the above, it decelerates but is moving to the left 26. The graph below shows the velocity of a race car moving along a straight line as a function of time. What is the magnitude of the displacement of the car from t = 2.0 seconds to t = 4.0 seconds? 20. m 40. m 60. m 80. m
27. Base your answer to the following question on the information and diagram below. A student standing on a knoll throws a snowball horizontally 4.5 meters above the level ground toward a smokestack 15 meters away. The snowball hits the smokestack 0.65 second after being released. [Neglect air resistance.] At the instant the snowball is released, the horizontal component of its velocity is approximately 6.9 m/s 9.8 m/s 17 m/s 23 m/s Base your answers to questions 28 and 29 on the information and diagram below. 30. The graph below represents the relationship between speed and time for a car moving in a straight line. A child kicks a ball with an initial velocity of 8.5 meters per second at an angle of 35 with the horizontal, as shown. The ball has an initial vertical velocity of 4.9 meters per second and a total time of flight of 1.0 second. [Neglect air resistance.] 28. The horizontal component of the ball's initial velocity is approximately 3.6 m/s 7.0 m/s 4.9 m/s 13 m/s 29. The maximum height reached by the ball is approximately 1.2 m 2.5 m 4.9 m 8.5 m The magnitude of the car's acceleration is 1.0 m/s 2 0.10 m/s 2 10 m/s 2 0.0 m/s 2
Base your answers to questions 31 through 34 on the following information. In the diagram below, a 10.-kilogram sphere, A, is projected horizontally with a velocity of 30. meters per second due east from a height of 20. meters above level ground. At the same instant, a 20.-kilogram sphere, B, is projected horizontally with a velocity of 10. meters per second due west from a height of 80. meters above level ground. [Neglect air friction.] 35. Note that the question below only has three choices. The diagram below represents the path of a stunt car that is driven off a cliff, neglecting friction. 31. Initially, the spheres are separated by a horizontal distance of 100. meters. What is the horizontal separation of the spheres at the end of 1.5 seconds? 15 m 30 m 40. m 45 m 32. Compared to the vertical acceleration of sphere A, the vertical acceleration of sphere B is the same twice as great one-half as great four times as great 33. The magnitude of the horizontal acceleration of sphere A is 0.0 m/s 2 2.0 m/s 2 9.8 m/s 2 15 m/s 2 34. Initially, the spheres are separated by a horizontal distance of 100. meters. What is the horizontal separation of the spheres at the end of 1.5 seconds? 15 m 30 m 40. m 45 m Compared to the horizontal component of the car's velocity at point A, the horizontal component of the car's velocity at point B is smaller greater the same 36. Two spheres, A and B, are simultaneously projected horizontally from the top of a tower. Sphere A has a horizontal speed of 40. meters per second and sphere B has a horizontal speed of 20. meters per second. Which statement best describes the time required for the spheres to reach the ground and the horizontal distance they travel? [Neglect friction and assume the ground is level.] Both spheres hit the ground at the same time and at the same distance from the base of the tower. Both spheres hit the ground at the same time, but sphere A lands twice as far as sphere B from the base of the tower. Both spheres hit the ground at the same time, but sphere B lands twice as far as sphere A from the base of the tower. Sphere A hits the ground before sphere B, and sphere A lands twice as far as sphere B from the base of the tower
37. The diagram represents a bicycle and rider traveling to the right at a constant speed. A ball is dropped from the hand of the cyclist. 40. Base your answer to the following question on the information and diagram below A golf ball leaves a golf club with an initial velocity of 40.0 meters per second at an angle of 40º with the horizontal. Which set of graphs best represents the horizontal motion of the ball relative to the ground? [Neglect air resistance.] 38. A ball is thrown horizontally from the top of a building with an initial velocity of 15 meters per second. At the same instant, a second ball is dropped from the top of the building. The two balls have the same path as they fall final velocity as they reach the ground initial horizontal velocity initial vertical velocity 39. A projectile is launched at an angle above the ground. The horizontal component of the projectile's velocity. vx, is initially 40. meters per second. The vertical component of the projectile's velocity, vy, is initially 30. meters per second. What are the components of the projectile's velocity after 2.0 seconds of flight? [Neglect friction.] vx = 40. m/s and vy = 10. m/s vx = 40. m/s and vy = 30. m/s vx = 20. m/s and vy = 10. m/s vx = 20. m/s and vy = 30. m/s What is the vertical component of the golf ball s initial velocity? 25.7 m/s 30.6 m/s 40.0 m/s 61.3 m/s 41. Four projectiles, A, B, C, and D, were launched from, and returned to, level ground. The data table below show the initial horizontal speed, initial vertical speed, and time of flight for each projectile. Which projectile traveled the greatest horizontal distance? [Neglect friction.] A B C D
Base your answers to questions 42 through 45 on the diagram and information below. A machine launches a tennis ball at an angle of 45 with the horizontal, as shown. The ball has an initial vertical velocity of 9.0 meters per second and an initial horizontal velocity of 9.0 meters per second. The ball reaches its maximum height 0.92 second after its launch. [Neglect air resistance and assume the ball lands at the same height above the ground from which it was launched.] 42. The speed at which the launcher fires tennis balls is constant, but the angle between the launcher and the horizontal can be varied. As the angle is decreased from 45 to 30., the range of the tennis balls decreases increases remains the same 43. The speed of the tennis ball as it leaves the launcher is approximately 4.5 m/s 8.3 m/s 13 m/s 18 m/s 44. The total horizontal distance traveled by the tennis ball during the entire time it is in the air is approximately 23 m 17 m 8.3 m 4.1 m 45. The speed at which the launcher fires tennis balls is constant, but the angle between the launcher and the horizontal can be varied. As the angle is decreased from 45 to 30., the range of the tennis balls decreases increases remains the same
46. Base your answer to the following question on the information and diagram below. A 60.-kilogram adult and a 30.-kilogram child are passengers on a rotor ride at an amusement park. When the rotating hollow cylinder reaches a certain constant speed, v, the floor moves downward. Both passengers stay "pinned" against the wall of the rotor, as shown in the diagram below. 48. Which graph best represents the relationship between the magnitude of the centripetal acceleration and the speed of an object moving in a circle of constant radius? Compared to the magnitude of the acceleration of the adult, the magnitude of the acceleration of the child is less greater the same 47. A 60.-kilogram adult and a 30.-kilogram child are passengers on a rotor ride at an amusement park. When the rotating hollow cylinder reaches a certain constant speed, v, the floor moves downward. Both passengers stay "pinned" against the wall of the rotor, as shown in the diagram below. Compared to the magnitude of the force acting on the adult, the magnitude of the force acting on the child is less greater the same
49. In the diagram below, S is a point on a car tire rotating at a constant rate. Which graph best represents the magnitude of the centripetal acceleration of point S as a function of time? Base your answers to questions 51 and 52 on the information and diagram below. The diagram shows a student seated on a rotating circular platform, holding a 2.0-kilogram block with a spring scale. The block is 1.2 meters from the center of the platform. The block has a constant speed of 8.0 meters per second. [Frictional forces on the block are negligible.] 50. An amusement park ride moves a rider at a constant speed of 14 meters per second in a horizontal circular path of radius 10. meters. What is the rider's centripetal acceleration in terms of g, the acceleration due to gravity? 1g 2g 3g 0g 51. Which statement best describes the block s movement as the platform rotates? Its velocity is directed tangent to the circular path, with an inward acceleration. Its velocity is directed tangent to the circular path, with an outward acceleration. Its velocity is directed perpendicular to the circular path, with an inward acceleration. Its velocity is directed perpendicular to the circular path, with an outward acceleration. 52. The reading on the spring scale is approximately 20. N 53 N 110 N 130 N
53. A car rounds a horizontal curve of constant radius at a constant speed. Which diagram best represents the directions of both the car s velocity, v, and acceleration, a? 54. The diagram below represents a ball undergoing uniform circular motion as it travels clockwise on a string. At the moment shown in the diagram, what are the correct directions of both the velocity and centripetal acceleration of the ball? 55. A rock dropped off a bridge takes 5 seconds to hit the water. Approximately what was the rock's velocity just before impact? 0 m/s 2 m/s 50 m/s 125 m/s 56. 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 57. If the mass of an object were doubled, its acceleration due to gravity would be halved doubled unchanged quadrupled 58. A -kilogram car travels at a constant speed of 20. meters per second around a horizontal circular track. The diameter of the track is meters. The magnitude of the car's centripetal acceleration is 59. A ball of mass M at the end of a string is swinging in a horizontal circular path of radius R at constant speed V. Which combination of changes would require the greatest increase in the centripetal force acting on the ball? doubling V and doubling R doubling V and halving R halving V and doubling R halving V and halving R Base your answers to questions 60 and 61 on the diagram below which shows a 2.0-kilogram cart traveling at a constant speed in a horizontal circle of radius 3.0 meters. The magnitude of the centripetal force of the cart is 24 Newtons. 60. In the position shown, the acceleration of the cart is 8.0 m/s 2 directed toward point A 8.0 m/s 2 directed toward point D 12 m/s 2 directed toward point A 12 m/s 2 directed toward point D 61. What is the speed of the cart? 6.0 m/s 16 m/s 36 m/s 4.0 m/s
Base your answers to questions 62 through 67 on the information and graph below. A machine fired several projectiles at the same angle,, above the horizontal. Each projectile was fired with a different initial velocity, vi. The graph below represents the relationship between the magnitude of the initial vertical velocity, viy, and the magnitude of the corresponding initial velocity, vi, of these projectiles 62. Determine the magnitude of the initial vertical velocity of the projectile, viy, when the magnitude of its initial velocity, vi, was 40. meters per second. 63. Determine the angle,, above the horizontal at which the projectiles were fired. 64. Determine the magnitude of the initial vertical velocity of the projectile, viy, when the magnitude of its initial velocity, vi, was 40. meters per second. [1] 65. Determine the angle,, above the horizontal at which the projectiles were fired. [1] 66. Calculate the magnitude of the initial horizontal velocity of the projectile, vix, when the magnitude of its initial velocity, vi, was 40. meters per second. [Show all work, including the equation and substitution with units.] [1] work [1] units 67. Calculate the magnitude of the initial horizontal velocity of the projectile, vix, when the magnitude of its initial velocity, vi, was 40. meters per second. [Show all work, including the equation and substitution with units.]