Base Your Answers to Questions 1 and 2 on the Graphs Below, Which Plot the Displacement of a Particle with Respect to Time

Home , Particle acceleration

Base your answers to questions 1 and 2 on the graphs below, which plot the displacement of a particle with respect to time.

5. The graph above represents the motion of an object traveling in a straight line as a function of time. What 1. In which of the following is the particle's acceleration is the average speed of the object during the first four constant? seconds? A) I only B) II only A) 0 m/s B) 0.2 m/s C) I and II only D) I, II, and III C) 0.5 m/s D) 1 m/s E) None of these E) 2 m/s 2. In which of the following is the rate of change of the particle's momentum zero? A) I only B) II only C) I and II only D) I, II, and III E) None of these

3. Base your answer to the following question on the graphs below, which plot the velocity of a particle with respect to time.

In which of these cases is the rate of change of the 6. A simple particle's displacement constant? pendulum oscillates with amplitude A and period T, as represented on the graph above. The nature of the A) I only B) II only velocity v and acceleration a of the object at time is C) III only D) I and II only best represented by which of the following? E) None of these A) v < 0, a < 0 B) v < 0, a = 0 4. Which pair of graphs represents the same C) v < 0, a > 0 D) v = 0, a > 0 1-dimensional motion? E) v = 0, a = 0 A) B) 7. An object undergoes constant acceleration. Initially at rest, the object travels 5 m in the first second. What additional distance will be covered in the next C) D) second? A) 5 m B) 10 m C) 15 m D) 20 m E) 25 m Base your answers to questions 10 and 11 on "the graph below which shows the velocity versus time for an object moving in a straight line.

8. The displacement x of an object moving in one dimension is shown above as a function of time t. The velocity of this object must be A) zero " B) constant and positive 10. During which interval does the particle have the C) constant and negative same average acceleration as 12 s < t < 14 s? D) increasing A) 0 s < t < 3 s B) 2 s < t < 5 s E) decreasing C) 3 s < t < 7 s D) 7 s < t < 10 s E) 9 s < t < 11 s 11. At what time after t = 0 does the object again pass through its initial position? A) 3 s B) 5 s C) 8.5 s D) 11 s E) 14 s

9. The displacement x of an object moving in one dimension is shown above as a function of time t. The acceleration of this object must be A) zero B) constant and positive C) constant and negative D) increasing E) decreasing Base your answers to questions 12 through 14 on 17. On another planet a ball is dropped and falls 10 "the position versus time graph below which shows meters in 4 seconds. Assuming uniform acceleration, the motion of a particle on a straight line. what is the acceleration neglecting air resistance? A) 0.625 m/s2 B) 1.25 m/s2 C) 2.5 m/s2 D) 5 m/s2 E) 10 m/s2 18. A car is driving 30 m/s and instantly stops. At this instant the driver releases a ball he was holding out the window. If the ball lands 2 seconds after released how far does the ball travel? Neglect air resistance. A) 15 m B) 30 m C) 60 m D) 900 m E) 1,800 m 19. A ball is dropped 4 meters above the surface of earth and the same ball is dropped on another planet with half the acceleration of gravity, what is the difference in the time it takes the balls to hit the " surface in seconds? 12. At which of the labeled points is the magnitude of A) B) the acceleration greatest? C) D) A) A B) B C) C D) D E) E E) 13. At which of the labeled points is the velocity zero? 20. Which of the Following is not a vector quantity? A) B only B) E only C) D only D) C and D A) Displacement B) Acceleration E) C and E C) Momentum D) Force E) Speed 14. At which of the labeled points is the magnitude of the velocity greatest? 21. A bullet is shot from a rifle. If the barrel is one meter long, and the muzzle velocity is 100 m/s, A) A B) B C) C D) D E) E which of the following quantities can we derive?

15. Which of the following reflects a change in A) The distance the bullet travels before landing acceleration? B) The average acceleration of the bullet C) The mass of the bullet A) A car traveling 20 m/s D) The energy of the bullet B) A car starting from rest rolling down an even E) The force exerted on the bullet ramp C) A motor scooter braking evenly from 10 m/s D) A skydiver in a vacuum E) A cyclist rolling down a parabolic hill 16. Two balls are dropped in a vacuum. If one is caught in half the time as the other what is the difference in distance the balls traveled? A) t B) t 2 C) t 2 D) 3 t E) 3 t2 22. Which is true of the motion of two free falling 27. A hammer and a feather are brought to the surface of objects of mass m and 2m dropped from equal the moon, where air resistance is negligible, and are heights d in a vacuum? released from the same height at rest. When the hammer hits the ground, the two objects will have A) Both objects land in the same time, but the the same heavier object has a greater final speed B) Both objects land in the same time, but the A) momentum lighter object has greater final speed B) kinetic energy C) Both objects land at the same time and both C) change in potential energy objects have the same final speed D) inertia D) Both objects have the same final speed, but the E) speed lighter object lands first 28. Which of the following is a vector quantity? E) Both objects have the same final speed, but the heavier object lands first A) speed B) potential energy 23. A motorist traveling 25m/s blows a red light. 5 C) time D) displacement seconds later a police officer parked at the corner, E) none of these begins pursuit on his motorcycle at 35 m/s. How 29. Which of the following is a scalar quantity? long does the chase last? A) linear momentum B) velocity A) 10 s B) 13 s C) 16 s D) 17 s E) 25 s C) acceleration D) kinetic energy 24. In 5 seconds a car accelerates from 0 to 40 m/s. 20 E) force seconds after reaching 40m/s the car comes to a 30. An object is dropped off a cliff of height h. When complete stop. If this deceleration takes 4 seconds, the object has fallen for 4 s, it has fallen a distance how far has the car traveled since its trip began? . How long will it take to fall A) 100 meters B) 800 meters the rest of the way? (Neglect air resistance) C) 980 meters D) 1,140 meters E) 1,700 meters A) 2.0 s B) 2.50 s C) 3.0 s D) 1.66 s 25. Object A and B are near the surface of the moon. When object A is released from rest, it falls a E) 4.50 s distance d in 2.0 seconds. Object B is twice the mass 31. An object is dropped of a cliff with a height of 8 m. of object A. How far would object B fall in 1.0 When the rock has been falling for 4 m, its velocity second if released from rest? is most nearly A) d B) d C) d D) d E) 2d A) 9 m/s B) 12 m/s 26. A softball is thrown straight up, reaching a C) 18 m/s D) 80 m/s maximum height of 20 meters. Neglecting air E) 320 m/s resistance, the vertical speed of the ball when it hits 32. An object is at rest. Which of the following must be the ground is true? A) 10 m/s B) 15 m/s I. Its linear momentum is zero. C) 20 m/s D) 30 m/s II. Its acceleration is zero. E) 40 m/s III. Its potential energy is not zero. A) I only B) I and II only C) I and III only D) I, II, and III E) None of these 33. An object is moving with constant acceleration. 38. A ball is released at rest, from a height of 5 m. Which of the following is necessarily true? About how long will it take for the ball to reach the I. The velocity is changing. ground? II. The kinetic energy is changing. A) 0.5 s B) 0.66 s III. The linear momentum is changing. C) 1 s D) 1.33 s A) I only B) II only E) 1.66 s C) I and II only D) I, II, and III 39. Which of the following is a scalar unit? E) None of these A) acceleration 34. An object has a non-zero acceleration. Of the following, which could be constant? B) speed I. speed C) displacement II. kinetic energy D) average velocity III. linear momentum E) instantaneous velocity A) I only B) I and II only 40. A car traveling at a speed of 10 m/s slows down to a C) I and III only D) II only speed of 2 m/s over a period of 4 s. The distance E) II and III only that the car has traveled is 35. An object has translational equilibrium if: A) 8 m B) 16 m C) 24 m D) 32 m E) 40 m I. It is at rest. 41. A train is traveling at a speed of 100 km/h. It then II. It has a constant velocity. brakes and comes to a halt over a distance of 70 m. III. It has a constant acceleration. The magnitude of the deceleration of the train is IV. It has a constant net force applied to it. nearest to A) I B) III A) 1.4 m/s2 B) 4.4 m/s2 C) I and II only D) III and IV only C) 5.5 m/s2 D) 7.1 m/s2 E) I, II, III and IV E) .71 m/s2 36. Two runners are facing each other 100 m apart. 42. A model aircraft requires a minimum speed of 15 They both run toward each other. One runner runs at m/s in order to take off. If accelerating from rest, a rate of 4 m/s and the other runs at a rate of 6 m/s. the minimum acceleration the airplane must have in How far has the 6 m/s runner traveled when he order to lift off of a 375 m long runway is closest to passes the other runner? A) 0.1 m/s2 B) 0.2 m/s2 A) 20 m B) 30 m C) 40 m D) 50 m E) 60 m C) 0.3 m/s2 D) 1.33 m/s2 37. An archer shoots an arrow straight up from the E) 9.8 m/s2 surface of the Earth. When the arrow reaches its 43. An object is dropped from Planet E. After 10 s, the maximum height , which of the following would be speed of the object is 40 m/s. What is the zero? acceleration due to gravity on this planet? I. speed II. velocity A) 2 m/s2 B) 4 m/s2 III. acceleration C) 6 m/s2 D) 8 m/s2 E) 10 m/s2 A) III only B) I and II only C) I and III only D) II and III only E) I, II, and III 44. A street car driver is traveling at a speed of 25 m/s 49. A gun fires a bullet directly upward. Which of the when he sees a road block. He applies the brakes following best characterizes its motion at the highest causing a magnitude of deceleration of 5 m/s2. If the point of its trajectory? roadblock is 70 m away, which of the following will A) Its velocity is downward and its acceleration is happen? upward. A) The car will hit the road block. B) Its velocity is upward and its acceleration is B) The car will stop immediately before the downward. roadblock. C) Both its velocity is and its acceleration are C) The car will stop 2.5 m before the roadblock. downward. D) The car will stop 5 m before the roadblock. D) Its velocity is zero and its acceleration is E) The car will stop 7.5 m before the roadblock. downward. 45. An object is released from rest on a planet that has E) Both its velocity and its acceleration are zero. no atmosphere. The object falls 8 m in the first 50. Which of the following statements are true? second. What is the acceleration due to gravity on the planet? I. An object with zero acceleration moves at a constant speed. A) 2 m/s2 B) 4 m/s2 II. An object with constant acceleration must move 2 2 C) 8 m/s D) 10 m/s in a straight line. 2 E) 16 m/s III. An object with an acceleration always 46. An object is thrown off a cliff with an initial upward perpendicular to its velocity must move in a circle. velocity of 15 m/s. It strikes the ground with a A) I, only B) II, only downward velocity of 25 m/s. If air resistance is C) I and III, only D) I, II, and III negligible, the height of the cliff is most nearly E) None of the above A) 10 m B) 20 m C) 30 m D) 40 m E) 50 m 51. A ball is thrown straight up with an initial velocity of 47. A car is traveling with a velocity of 5 m/s along a 14 m/s. The maximum height attained by the ball is straight road. Another car starting at rest 250 m closest to behind it begins to accelerate uniformly. What is the magnitude of its acceleration if it catches the first car A) 0.7 m B) 1.4 m after 10 seconds? C) 10 m D) 20 m E) 30 m A) 0.5 m/s2 B) 1 m/s2 C) 2 m/s2 D) 2.5 m/s2 52. An airplane traveling at 52 m/s slows to 32 m/s in a time span of 4 s. What is the magnitude of its E) 6 m/s2 average acceleration? 48. A car is traveling along a straight road with a 2 2 velocity of 10 m/s. It begins to accelerate uniformly A) 5 m/s B) 8 m/s 2 2 at time t = 0 and covers a distance of 300 m in 5 s. C) 13 m/s D) 20 m/s What is the magnitude of the acceleration? E) 52 m/s2 A) 10 m/s2 B) 12 m/s2 53. A train starts at rest and accelerates at a uniform rate 2 C) 20 m/s2 D) 24 m/s2 of 4 m/s . Which of the following is closest to its speed after it has traveled 25 meters? E) 60 m/s2 A) 10 m/s B) 14 m/s C) 70 m/s D) 100 m/s E) 200 m/s 54. An airplane initially at rest accelerates at a constant 60. A truck moving along a straight road at 30 m/s rate of 6 m/s2. When its speed is 30 m/s, the applies its breaks such that its velocity is given by distance it has traveled is closest to the equation v(t) = 30 – 2t, where v is in m/s and t is in seconds. What is the truck's acceleration at t = 1 A) 5 m B) 38 m s? C) 75 m D) 150 m E) 180 m A) –30 m/s2 B) –2 m/s2 C) 2 m/s2 D) 15 m/s2 55. A motorist driving at 50 m/s applies the brakes so 2 that the car decelerates at a rate of 2 m/s2. The time E) 30 m/s for the car to stop is closest to 61. An object's motion is given by the equation x(t) = 4t + 4t3. What is the equation for the object's A) 5 s B) 10 s C) 13 s D) 25 s E) 50 s acceleration? 56. A car traveling at 30 m/s decelerates uniformly to 20 m/s in 300 m. The amount of time it took to A) a(t) = 24t B) a(t) = 24t + 4 4 2 2 decelerate is closest to C) a(t) = t + 2t D) a(t) = 4t + 4 E) a(t) = 12t 2 + 4 A) 5 s B) 6 s C) 10 s D) 12 s E) 30 s 62. An object's motion is given by the equation 57. The graph of the acceleration of an object is shown x(t) = 2 + 4t3 . What is the equation for the object's below. velocity? A) v(t) = 2t + 12t 2 B) v(t) = 4t 2 C) v(t) = 2/t + 4t 2 D) v(t) = 2t + t4 E) v(t) = 12t 2 63. The position of a particle moving along the x-axis is given by the equation x(t) = 2 + 6t2 , where x is in meters and t is in seconds. What is the average The highest order term in the equation for the velocity during the interval t = 0 to t = 0.5? position of this object has what sign and what exponent of t? A) 2 m/s B) 3 m/s C) 4 m/s D) 5 m/s E) 6 m/s A) + 1 B) – 1 C) + 2 D) – 2 E) + 3 64. The position of a particle moving along the x-axis is given by the equation x(t) = 1 + 2t2 + 3t3 , where x is 58. What is the change in velocity in the interval t = 0 in meters and t is in seconds. What is the average to t = of an object whose acceleration is given by a acceleration during the interval t = 0 to t = 1? (t) = cos 2t? A) 6 m/s2 B) 9 m/s2 A) 0 m/s B) 0.5 m/s C) 13 m/s2 D) 18 m/s2 C) 1 m/s D) – 0.5 m/s E) 22 m/s2 E) – 1 m/s 65. The velocity of a particle moving along the x-axis is 59. The equation for the position x of a particle whose given by the equation v(t) = 1 + 5t + 2t2 , where v is acceleration is given by the equation a(t) = 6t – 3 in m/s and t is in seconds. What is the average and starts at rest from the origin is acceleration during the interval t = 0 to t = 2? 2 2 A) x(t) = 3t – 3t B) x(t) = 6t – 3t A) 9 m/s2 B) 10 m/s2 3 2 3 C) x(t) = t – 3t /2 D) x(t) = 6t – 3t C) 13 m/s2 D) 18 m/s2 3 E) x(t) = 3t – t E) 19 m/s2 66. The velocity of a particle moving along the x-axis is 72. The equation v(t) = 3t2 – 4t + 2, where v is in meters given by the equation v(t) = 5 + 3t2 , where v is in per second and t is in seconds; gives the velocity of a m/s and t is in seconds. What is the average velocity vehicle moving along a straight track. The vehicle’s during the interval t = 0 to t = 3? initial position is 3 m. What is the vehicle’s position at t = 4 s? A) 12 m/s B) 14 m/s C) 28 m/s D) 31 m/s A) 40 m B) 41 m C) 42 m D) 43 m E) 44 m E) 42 m/s 73. The position of a vehicle moving on a straight track 67. An object moves along the x-axis with a velocity along the x-axis is given by the equation v(t) = 3t2 – 2t – 3, where v is in m/s and t is in x(t) = t2 + 3t + 5, where x is in meters and t is in seconds. What is the total distance traveled during seconds. What is its acceleration at time t = 5 s? the time interval 2 < t < 5 s? A) Zero B) 2 m/s2 A) 80 m B) 83 m C) 85 m D) 87 m E) 90 m C) 5 m/s2 D) 10 m/s2 2 68. The equation of the position of an object moving E) 13 m/s along the x-axis is given by x(t) = 1.5t3 – 4.5t2 + .5t, 74. The velocity of a car traveling on a straight track where x is in meters and t is in seconds. What is the along the y-axis is given by the equation object’s displacement when its instantaneous v(t) = –12t2 + 6t + 2, where v is in meters per second acceleration is equal to zero? and t is in seconds. The vehicle’s initial position is y = –1 m. At which one of the following times is the A) Zero B) –2.5 m car at the origin? C) 3 m D) –12 m E) 12 m A) Zero B) 1 s C) 2 s D) 3 s E) 4 s 69. The velocity of a car traveling along the y-axis is 75. The position of a vehicle moving on a straight track given by the equation v(t) = 2t2 – 8t + 9, where v is in along the x-axis is given by the equation meters per second and t is in seconds. At what time x(t) = 3t3 – 2t2 + t, where x is in meters and t is in is the car’s instantaneous acceleration equal to zero? seconds. What is its velocity at time t = 3 s? A) Zero B) 1 s C) 2 s D) 3 s E) 4 s A) 47 m/s B) 50 m/s C) 60 m/s D) 66 m/s 70. The acceleration of a car traveling on a straight track along the x-axis is given by the equation a(t) = 2t + 1 E) 70 m/s , where a is in meters per second squared and t is in 76. Which of the following is not true about the path of seconds. If x(0) = 0 and v(0) = 0, what is the car's a canon ball launched horizontally from the earth’s displacement at t = 3? surface if air resistance is neglected? A) 1 m B) 7 m A) The cannonball has a uniform horizontal C) 9 m D) 12 m velocity E) 13.5 m B) The total velocity of the cannonball increases as a function of time 71. The acceleration of a car traveling on a straight track along the y-axis is given by the equation a = 5 m/s2, C) The vertical velocity of cannonball increases as where a is in meters per second squared. If at t = 0 s a function of time the car’s velocity is 3 m/s, what is its velocity at t = D) The distance the cannonball travels only 2 s? depends upon the height it is shot from E) The distance the cannonball travels is A) 3 m/s B) 5 m/s dependent on its mass C) 10 m/s D) 13 m/s E) 15 m/s 77. A ball on a table of height h is rolled off a table 82. A person throws a ball at an angle of 30o with the traveling at velocity v, neglecting air resistance how horizontal with a velocity of 32 m/s. As the ball is much time does it take for the ball to hit the ground? thrown, a second person is running past the thrower at a constant velocity. At what velocity must this A) B) C) D) E) second person run so that she may catch the ball as it hits the ground? 78. A skydiver wishes to play catch with her friend. If the thrower jumps 5 seconds after the catcher and A) 32 m/s B) 32sin 30o m/s the horizontal component of their distance is 5 C) 32cos 30o m/s D) 32tan 30o m/s meters, what angle with the horizontal must the ball E) 64cos 30o m/s be thrown to complete the pass? Neglect air Base your answers to questions 83 through 85 on resistance. "the following diagram, in which a ball of mass m is A) Arctan(25) B) Arctan(1/125) rolled horizontally off a table of height h and lands a C) Arccos(1/125) D) Arctan(1/5) distance D from the edge of the table. E) Arccos(25) 79. A basketball is thrown upwards on an arc at a 60 degree angle with the horizontal. If the velocity of the ball is 5 m/s how fast must the thrower run to catch the ball after it is released? A) 2.5 m/s B) 4.3 m/s C) 5.0 m/s D) 10 m/s E) 20 m/s 80. A snowball is thrown out the window of a car moving at 20 m/s. The ball is thrown vertically to hit " a snowman 20 meters away at window level. What 83. If the initial horizontal velocity of the ball is speed would the snowball need to be thrown to hit represented as the quantity v, what is the kinetic the snowman? energy of the ball right before it hits the ground? A) 2.5 m/s B) 4.9 m/s A) B) C) 9.8 m/s D) 14.7 m/s C) D) E) 19.6 m/s E) 81. Rocky the Flying Squirrel is carrying a nut of mass 84. What is the initial horizontal velocity of the ball? 0.5 kg while flying horizontally at a height of 15 m above the ground at a speed of 12 m/s. Bullwinkle A) B) is eagerly awaiting the delivery of the nut on the ground. Rocky releases the nut as he is directly C) 2Dh/g D) Dhg above Bullwinkle. How far from Bullwinkle will E) the nut land if Bullwinkle does not move? 85. How much time elapses between the time the ball A) 3 m B) 3 m leaves the edge of the table to when hits the ground? C) 6 m D) 6 m A) hD B) h/D E) 12 m C) hD/g D) 2h/g E) 86. A baseball player throws a ball horizontally. Which 88. A projectile is fired with an initial velocity v0 at an statement best describes the ball's motion after it is initial angle q 0 with the horizontal. Which of the thrown? [Neglect the effect of friction.] following pairs of graphs below best represents the A) Its vertical speed remains the same, and its horizontal components of the velocity, v, and horizontal speed increases. acceleration, a, of the projectile as functions of time? B) Its vertical speed remains the same, and its horizontal speed remains the same. A) C) Its vertical speed increases, and its horizontal speed increases. D) Its vertical speed increases, and its horizontal speed remains the same. B) E) Its vertical speed increases and its horizontal speed decreases. 87. The diagram below shows a projectile moving with C) speed v at the top of its trajectory.

Which vector best represents the acceleration of the projectile in the position shown? A) B)

C) D) Base your answers to questions 89 and 90 on the Base your answers to questions 93 and 94 on the information below. following information.

A projectile is launched from ground level with an From a cliff of height 28.8 m above the ground, a initial velocity of v at an angle q above the ball is thrown horizontally with an initial velocity of horizontal. Ignore air resistance. 7 m/s. 89. The maximum horizontal displacement of the 93. What is the range of the ball? projectile is A) 4.2 m B) 8.4 m A) vsin 2q C) 12.6 m D) 16.8 m g E) 22.4 m 2 B) (vsin q) g 94. The magnitude of the velocity of the ball when it C) vsin 2q strikes the ground is most nearly 2g 2 A) 15 m/s. B) 20 m/s. D) (vsin q) 2g C) 25 m/s. D) 30 m/s. E) v2sin 2q g E) 35 m/s. 90. The maximum vertical displacement of the projectile 95. An object moving horizontally with speed v falls off is the edge of a vertical cliff and lands a distance d A) vsin 2q from the base of the cliff. How far from the base of g the cliff would the object land if the height of the 2 cliff was doubled? B) (vsin q) g C) vsin 2q A) d B) d 2g C) 2d D) 2 d D) (vsin q)2 2g E) 4d E) 2vsin 2q 96. An object moving horizontally with speed v falls off g the edge of a vertical cliff and takes a time t to land. How long would it take for the object to land if it Base your answers to questions 91 and 92 on the was moving with a horizontal velocity 2v? following information. A) t A ball is thrown horizontally 20 m above the ground B) t with a velocity of 5 m/s. C) t 91. How far from the base of the cliff will the ball land? D) 2t E) It could not be determined unless the height of A) 5.6 m B) 9.2 m the cliff was known C) 10 m D) 12 m E) 18.4 m 92. How much time will pass before the ball hits the ground? A) 2 s B) 2.8 s C) 4.6 s D) 6 s E) 9.2 s 97. An object moving horizontally with speed v falls off the edge of a vertical cliff and lands a distance d from the base of the cliff. If it had landed a distance 2d from the base of the cliff, how fast would the object had to have been moving? A) v B) v C) 2v D) 4v E) It cannot be determined unless the height of the cliff is known 98. Base your answer to the following question on the information below.

A 4.0 kg block rests at the edge of a platform that is 20 m above level ground. The block is launched horizontally with an initial velocity of 15 m/s. The time it would take to reach the ground is most nearly A) 1.33 s B) 1.41 s C) 1.73 s D) 2.0 s E) 2.5 s Base your answers to questions 99 through 103 on the following information.

A cannonball is fired and follows the parabolic path shown below. Air resistance is negligible. Point B is the highest point on the path and points A and C are at the same height.

99. Which of the following best describes the direction of the net force on the ball at point A? A) up and to the right B) to the right C) down and to the right D) down E) There is no net force on the cannonball at point A 100. Which of the following best describes the direction of the velocity of the cannonball at point B? A) to the right B) up and to the right C) down and to the right D) up E) down 101. Which of the following best describes the direction of the acceleration of the ball at point C? A) to the right B) down and to the right C) down D) up and to the right E) up and to the left 102. How do the accelerations of the ball at the three points compare?

A) aA < aB < aC B) aB < aA < aC C) aA = aB = aC D) aA = aB < aC E) aB < aA = aC 103. How do the speeds of the cannonball at the there points compare?

A) vA < vB < vC B) vC < vB < vA C) vB < vA < vC D) vA < vB = vC E) vB < vA = vC

104. A cannon fires a cannonball with an initial velocity 108. A cannon fires a projectile with an initial speed v at of 30 m/s at an angle of 60º to the horizontal. If air an angle q above the horizon. What is the resistance is negligible, the amount of time the horizontal distance traveled by the projectile? cannonball remains in the air is A) v2sin q A) 2.6 s B) 3.0 s C) 5.2 s D) 6.0 s E) 7.8 s g 105. An object is thrown off of a cliff 320 m above level B) 2v2sin q ground with an initial horizontal velocity of 20 m/s. g The amount of time it takes to strike the ground is C) v2sin2 q most nearly g 2 A) 2 s B) 4 s C) 8 s D) 12 s E) 16 s D) 2v sin2 q g 106. A ball is launched from ground level with an initial E) 2v2sin2 q upwards velocity of 20 m/s and an initial horizontal g velocity of 30 m/s. How far from its starting position does the ball land assuming the ground is 109. A cannon fires a projectile with an initial speed v at level? an angle q above the horizon. What is the maximum height reached by the projectile? A) 30 m B) 60 m C) 120 m D) 150 m A) 2v2sin2 q E) 180 m g B) v2sin2 q 107. A ball is thrown horizontally out of a hot air 2g balloon at a height of 500 m above level ground 2 with an initial velocity of 15 m/s. If air resistance C) 2v cos q sin q is negligible, the time that it will take the ball to g reach the ground is most nearly D) v2cos q sinq g A) 3 s B) 5 s C) 10 s D) 15 s E) 33 s E) v2cos2 q g 110. A cannon fires a projectile with an initial speed v at Base your answers to questions 115 and 116 on the an angle q above the horizon. At what time does following information. the projectile hit the ground? An object is thrown off a cliff above level ground A) 2vcos q with an initial horizontal velocity of 15 m/s. It takes g 4 seconds for the object to reach the ground. B) vcos q 115. If air resistance is negligible, the distance from the g base of the cliff that the object lands is most nearly C) 2vsin q g A) 60 m B) 80 m D) vsin q C) 120 m D) 160 m g E) 240 m E) vsin2 q 116. If air resistance is negligible, the height of the cliff g is most nearly Base your answers to questions 111 and 112 on the A) 60 m B) 80 m following information. C) 120 m D) 160 m E) 240 m An object is thrown with a horizontal velocity of 15 m/s off of a cliff that is 180 m above level ground. 117. A plane is traveling north at 200 m/s; a wind blows 111. If air resistance is negligible, the distance between from the west and accelerates the plane at 15 m/s the base of the cliff and the place where the object 2. If the wind lasts 10 seconds what is the planes new velocity? reaches the ground is most nearly A) 250 m/s 53 degrees north of east A) 50 m B) 60 m B) 250 m/s north C) 150 m D) 180 m C) 350 m/s north E) 90 m D) 350 m/s 37 degrees north of east 112. If air resistance is negligible, the time it takes the E) 50 m/s north object to reach the ground is most nearly 118. Which of the following paths has the least A) 4 s B) 5 s C) 6 s D) 7 s E) 8 s displacement? A) 40 meters north, 12 meters east, 30 meters 113. An object is thrown horizontally off of a 125 m south, and 15 meters west high cliff above level ground with an initial velocity B) 5 meters west 4 meters east of 15 m/s. If air resistance is negligible, the distance from the base of the cliff to the point C) 16 meters north 2 meters south east where the object lands is most nearly D) 3 meters south east E) 3 meters north, 4 meters east, and 5 meters 37 A) 25 m B) 45 m degrees south of west C) 75 m D) 90 m 119. A mail courier is being chased by a dog. In an E) 150 m effort to tire the dog out before getting to the next 114. An object is thrown off of a cliff above ground house 10 meters away, he runs in the path of an level with an initial upward velocity of 6 m/s, and isosceles triangle making one 60 degree vertex how an initial horizontal velocity of 15 m/s. It takes 3 s far will he run? for it to reach the ground. If air resistance is neglected, the height of the cliff is most nearly A) 10 meters B) 20 meters C) 30 meters D) 40 meters A) 18 m B) 27 m C) 45 m D) 63 m E) 90 m E) 60 meters 120. A boat traveling at 20m/s travels east for 20 124. A truck traveled 1200 meters south in 80 seconds seconds, west for 5 seconds, north for 22 seconds and then 500 meters west in 20 seconds. The and south for 2 seconds. What is the boats total magnitude of the average velocity of the truck is displacement? most nearly A) 200 m B) 300 m A) 10 m/s B) 13 m/s C) 400 m D) 500 m C) 17 m/s D) 25 m/s E) 800 m E) 30 m/s 121. A plane is traveling at 230 m/s. A battle ship 125. A ship can travel at a maximum speed of 8 km/h in 10,000 meters below fires a missile which travels at any direction in still water. What is the maximum a constant 300 m/s while the plane is directly velocity of the ship relative to the shore if it is overhead. If the missile is to hit what angle should moving perpendicular to a 6 km/h current? it be shot with the horizontal? A) 4 km/h B) 6 km/h A) Arcsine(23/30) B) Arctan(23/30) C) 8 km/h D) 9 km/h C) Arccos(5/3) D) Arccos(23/30) E) 10 km/h E) Arccos(30/23) 122. Base your answer to the following question on the picture below which shows the direction of motion of an object.

126. In still water a ship can produce a maximum velocity of 5 If the object moves with a constant speed v along m/s in any direction. This same ship is placed in a the path shown, what is the direction of the net river with a current of 5 m/s eastward. With what acceleration that acted on the object at the velocity should the boat be operated with in order beginning of the path? to reach point Y from point X? (Note: Point Y is due north of point X) A) B) A) 5 m/s due West until the ship is far enough C) D) out, then 5 m/s due North. B) Simultaneously, 2.5 m/s due West and 2.5 m/s due North. E) C) 5 m/s due North. D) 5 m/s due North until the ship has reached the northern shore. Then 5 m/s due West until the ship reaches point Y. 123. A car, starting from rest, experiences a constant acceleration for 5 seconds such that it moves 200 m E) The ship's engine is not powerful enough to west and 150 m north. What was the magnitude of reach point Y. this acceleration? 127. A ship travels 5 miles due east and then 12 miles A) 5 m/s2 B) 10 m/s2 due north. What is the net displacement of the ship? C) 20 m/s2 D) 40 m/s2 E) 100 m/s2 A) 7 miles B) 13 miles C) 16 miles D) 17 miles E) 19 miles 132. The shape of the path of a projectile launched at some angle above the horizontal is mostly nearly A) circular B) elliptical C) hyperbolic D) parabolic E) linear 128. A bicycle moves at constant speed over a hill along 133. The velocity of an object is given by v(t) = 2ti + 4j a smoothly curved surface as shown above. Which . What is the acceleration of the object at t = 3 s if of the following best describes the directions of the it starts at (0,2)? velocity and the acceleration at the instant it is at A) 2 m/s2 B) 4 m/s2 the highest position? C) 8 m/s2 D) 12 m/s2 A) The velocity is towards the right of the page E) 16 m/s2 and the acceleration is towards the top of the 134. What is the magnitude of the acceleration of an page. object whose position is given by the equation x(t) B) The velocity is towards the right of the page = 3t2 – 3t and y(t) = 3t2 – 3t? and the acceleration is towards the bottom of the page. A) 6 m/s2 B) 6 m/s2 C) The velocity is towards the right of the page C) 12 m/s2 D) 12 m/s2 and the acceleration is towards the bottom E) 36 m/s2 right of the page. 135. The velocity of a projectile is given by the two D) The velocity is towards the right of the page equations vy(t) = –10t + 30 and vx(t) = 15, where vy and the acceleration is towards the top right of and vx are in m/s and t is in seconds. What the page. horizontal distance has the projectile traveled when E) The velocity is towards the top right of the the projectile is at its maximum height? page and the acceleration is towards the bottom right of the page. A) 3 m B) 15 m C) 45 m D) 90 m 129. An object is moving in the xy-plane according to E) 120 m the equations x(t) = 3sin(3t) and y(t) = 4cos(3t). What is the maximum magnitude of the particle's 136. The motion of a projectile is given by the two acceleration? equations, x(t) = 60t and y(t) = –5t2 + 20, where x and y are in meters and t is in seconds. What is the 2 2 A) 5 m/s B) 15 m/s projectile's speed at t = 8 s? C) 30 m/s2 D) 36 m/s2 E) 45 m/s2 A) 20 m/s B) 40 m/s C) 60 m/s D) 80 m/s 130. If an object moves with non-zero, constant E) 100 m/s accelerations in two dimensions which are equal in magnitude, its path is 137. The acceleration of a particle that begins at rest at the origin is given by a(t)= 3ti + 4tj, where a is in A) linear B) hyperbolic m/s2 and t is in seconds. The particle’s distance C) elliptical D) parabolic from the origin at time t = 2 s is most nearly E) circular A) 6 m B) 7 m C) 8 m D) 9 m E) 10 m 131. The path of an object that moves with a constant acceleration in the x-direction and zero acceleration in the y-direction is A) circular B) hyperbolic C) parabolic D) elliptical E) linear 138. Two cars initially at the origin begin moving with 141. An object moves in the xy-plane according to the velocities v1(t) = (2i + 3j) and v2(t)= (-i + j) where equations x(t)= t3 and y = cost where x and y are in both velocities are in m/s. What is the rate at meters and t is in seconds. What is the magnitude which the distance between the cars is increasing? of its velocity at t = p s? A) m/s B) m/s A) Zero B) 1 C) p 3 D) 3p 2 E) 9p 4 C) 5 m/s D) m/s 142. The motion of a car is described as E) 25 m/s x(t) = 3t2 – 4t + 5 and y(t) = 4t2 + 3t – 4, where x 139. A particle is moving along the curve y = x3 + 2x and y are in meters and t is in seconds. What is the with a constant x-component of velocity of 4 m/s. car’s acceleration at t = 15 s? What is the y-component of its velocity at x = 2 m? A) Zero B) 5 m/s2 A) 4 m/s B) 14 m/s C) 10 m/s2 D) 15 m/s2 C) 32 m/s D) 56 m/s E) 20 m/s2 E) 64 m/s 140. An object moves in the xy-plane with a velocity given by v(t) = 3t2i + 4sin2tj where x and y are in meters and v is in meters per seconds. What is its displacement between t = 0 and t = 2 s? A) 8i – 2(cos 2)j B) 8i – 2(cos 4)j C) 8i + 2(cos 2)j D) 8i + 2(cos 4)j E) 12i + 4(sin 4)j Answer Key kinematics review

1. D 37. B 73. B 109. B 2. C 38. C 74. B 110. C 3. B 39. B 75. E 111. E 4. C 40. C 76. E 112. C 5. C 41. C 77. E 113. C 6. D 42. C 78. A 114. B 7. C 43. B 79. A 115. A 8. B 44. E 80. B 116. B 9. A 45. E 81. E 117. A 10. D 46. B 82. C 118. E 11. C 47. E 83. D 119. B 12. E 48. C 84. A 120. D 13. E 49. D 85. E 121. D 14. D 50. C 86. D 122. E 15. E 51. C 87. D 123. C 16. E 52. A 88. C 124. B 17. B 53. B 89. E 125. E 18. C 54. C 90. D 126. E 19. A 55. D 91. C 127. B 20. E 56. D 92. A 128. B 21. B 57. E 93. D 129. D 22. C 58. A 94. C 130. A 23. B 59. C 95. B 131. C 24. B 60. B 96. C 132. D 25. B 61. A 97. C 133. A 26. C 62. E 98. D 134. B 27. E 63. B 99. D 135. C 28. D 64. C 100. A 136. E 29. D 65. A 101. C 137. B 30. D 66. B 102. C 138. D 31. A 67. D 103. E 139. B 32. A 68. B 104. C 140. B 33. D 69. C 105. C 141. D 34. B 70. E 106. C 142. C 35. C 71. D 107. C 36. E 72. D 108. C