Midterm Review
1. When an object moves with constant velocity, does its average velocity during any time interval differ
from its instantaneous velocity at any instant? Explain.
2. In which of the following cases does a car have a negative velocity and a positive acceleration? A car
that is traveling in the
(a) –x direction at a constant 20 m/s.
(b) –x direction increasing in speed.
(c) +x direction increasing in speed.
(d) –x direction decreasing in speed.
(e) +x direction decreasing in speed.
3. A baseball pitcher throws a baseball with a speed of 43 m/s. Estimate the average acceleration of the ball
during the throwing motion. In throwing the baseball, the pitcher accelerates it through a displacement
of about 3.5 m, from behind the body to the point where it is released.
4. (II) Figure 2–42 shows the velocity of a train as a function of time. (a) At what time was its velocity
greatest? (b) During what periods, if any, was the velocity constant? (c) During what periods, if any, was
the acceleration constant? (d) When was the magnitude of the acceleration greatest?
5. (II) The position of a rabbit along a straight tunnel as a function of time is plotted in Fig. 2–44. What is
its instantaneous velocity (a) at t = 10.0 s and (b) at t = 30.0 s? What is its average velocity (c) between t
= 0 and t = 5.0 s, (d) between t = 25.0 s and t = 30.0 s, and (e) between t = 40.0 s and t = 50.0 s?
6. (II) In Fig. 2–44, (a) during what time periods, if any, is the velocity constant? (b) At what time is the
velocity greatest? (c) At what time, if any, is the velocity zero? (d) Does the object move in one
direction or in both directions during the time shown?
7. (III) Sketch the v vs. t graph for the object whose displacement as a function of time is given by Fig. 2–
44.
8. Which of the following situations is impossible?
(a) An object has velocity directed east and acceleration directed west.
(b) An object has velocity directed east and acceleration directed east.
(c) An object has zero velocity but non-zero acceleration.
(d) An object has constant non-zero acceleration and changing velocity.
(e) An object has constant non-zero velocity and changing acceleration.
9. If the velocity of an object is zero at one instant, what is true about the acceleration of that object?
(There could be more than one correct choice.)
(a) The acceleration could be positive.
(c) The acceleration could be zero.
(b) The acceleration could be negative.
(d) The acceleration must be zero.
10. A rock from a volcanic eruption is launched straight up into the air with no appreciable air resistance.
Which one of the following statements about this rock while it is in the air is correct?
(a) On the way up, its acceleration is downward and its velocity is upward, and at the highest point both
its velocity and acceleration are zero.
(b) On the way down, both its velocity and acceleration are downward, and at the highest point both its
velocity and acceleration are zero.
(c) Throughout the motion, the acceleration is downward, and the velocity is always in the same
direction as the acceleration.
(d) The acceleration is downward at all points in the motion.
(e) The acceleration is downward at all points in the motion except that is zero at the highest point.
11. A 10-kg rock and a 20-kg rock are thrown upward with the same initial speed v0 and experience no
significant air resistance. If the 10-kg rock reaches a maximum height h, what maximum height will the
20-kg ball reach?
(a) h/4
(b) h/2
(c) h
(d) 2h
(e) 4h
12. A 10-kg rock and 20-kg rock are dropped from the same height and experience no significant air
resistance. If it takes the 20-kg rock a time T to reach the ground, what time will it take the 10-kg rock to
reach the ground?
(a) 4T
(b) 2T
(c) T
(d) T/2
(e) T/4
13. From the edge of a roof top you toss a green ball upwards with initial speed v0 and a blue ball
downwards with the same initial speed. Air resistance is negligible. When they reach the ground below
(a) the green ball will be moving faster than the blue ball.
(b) the blue ball will be moving faster than the green ball.
(c) the two balls will have the same speed.
14. An object is moving with constant non-zero velocity in the +x direction. The position versus time graph
of this object is
(a) a horizontal straight line.
(b) a vertical straight line.
(c) a straight line making an angle with the time axis.
(d) a parabolic curve.
15. An object is moving with constant non-zero acceleration in the +x direction. The position versus time
graph of this object is
(a) a horizontal straight line.
(c) a straight line making an angle with the
(b) a vertical straight line.
time axis.
(d) a parabolic curve.
16. An object is moving with constant non-zero velocity in the +x direction. The velocity versus time graph
of this object is
(a) a horizontal straight line.
(b) a vertical straight line.
(c) a straight line making an angle with the time axis.
(d) a parabolic curve.
17. Which of the following graphs represent an object at rest? (There could be more than one correct
choice.)
a. graph a
b. graph b
c. graph c
d. graph d
e. graph e
18. Which of the following graphs represent an object having zero acceleration?
(a) only graph a
(b) only graph b
(c) graphs a and b
(d) graphs b and c
(e) graphs c and d
19. The figure shows a graph of the position x of two cars, C and D, as a function of time t.
According to this graph, which statements about these cars must be true? (There could be more than one
correct choice.)
(a) The magnitude of the acceleration of car C is greater than the magnitude of the acceleration of car D.
(b) The magnitude of the acceleration of car C is less than the magnitude of the acceleration of car D.
(c) At time t = 10 s, both cars have the same velocity.
(d) Both cars have the same acceleration.
(e) The cars meet at time t = 10 s.
20. The graph in the figure shows the position of an object as a function of time. The letters H-L represent
particular moments of time.
(a) At which moment in time is the speed of the object the greatest?
(b) At which moment in time is the speed of the object equal to zero?
21. The graph in the figure shows the position of a particle as it travels along the x-axis.
At what value of t is the speed of the particle equal to 0 m/s?
(a) 0 s
(b) 1 s
(c) 2 s
(d) 3 s
(e) 4 s
22. For general projectile motion with no air resistance, the horizontal component of a projectile's velocity
(a) remains zero.
(d) continuously decreases.
(b) remains a non-zero constant.
(e) first decreases and then increases.
(c) continuously increases.
23. For general projectile motion with no air resistance, the horizontal component of a projectile's
acceleration
(a) is always zero.
(d) continuously decreases.
(b) remains a non-zero constant.
(e) first decreases and then increases.
(c) continuously increases.
24. For general projectile motion with no air resistance, the vertical component of a projectile's acceleration
(a) is always zero.
(d) continuously decreases.
(b) remains a non-zero constant.
(e) first decreases and then increases.
(c) continuously increases.
25. Which of the following statements are true about an object in two-dimensional projectile motion with no
air resistance? (There could be more than one correct choice.)
(a) The speed of the object is constant but its velocity is not constant.
(b) The acceleration of the object is +g when the object is rising and -g when it is falling.
(c) The acceleration of the object is zero at its highest point.
(d) The speed of the object is zero at its highest point.
(e) The horizontal acceleration is always zero and the vertical acceleration is always a non-zero constant
downward.
26. A pilot drops a package from a plane flying horizontally at a constant speed. Neglecting air resistance,
when the package hits the ground the horizontal location of the plane will
(a) be behind the package.
(b) be directly over the package.
(c) be in front of the package.
(d) depend on the speed of the plane when the package was released.
27. A stone is thrown horizontally with an initial speed of 10 m/s from the edge of a cliff. A stopwatch
measures the stone's trajectory time from the top of the cliff to the bottom to be 4.3 s. What is the height
of the cliff if air resistance is negligibly small?
(a) 22 m
(b) 43 m
(c) 77 m
(d) 91 m
28. A girl throws a rock horizontally, with a velocity of 10 m/s, from a bridge. It falls 20 m to the water
below. How far does the rock travel horizontally before striking the water, assuming negligible air
resistance?
(a) 14 m
(b) 16 m
(c) 20 m
(d) 24 m
29. A projectile is fired from ground level on a horizontal plain. If the initial speed of the projectile is now
doubled, and we neglect air resistance,
(d) its range will quadruple.
(a) its range will be increased by .
(e) its range will decrease by a factor of four.
(b) its range will double.
(c) its range will be decreased by a factor of two.
30. An object is dropped from rest into a pit, and accelerates due to gravity at roughly 10 m/s2. It hits the
ground in 5 seconds. A rock is then dropped from rest into a second pit, and hits the ground in 10
seconds. How much deeper is the second pit, compared to the first pit? Neglect air resistance.
(a) four times deeper
(b) two times deeper
(c) three times deeper
(d) five times deeper
FORCES
31. A girl attaches a rock to a string, which she then swings counter-clockwise in a horizontal circle. The
string breaks at point P in the figure, which shows a bird's-eye view (as seen from above). Which path
(A-E) will the rock follow?
(a) Path A
(b) Path B
(c) Path C
(d) Path D
(e) Path E
32. A satellite is in orbit around the earth. Which one feels the greater force?
(a) the satellite because the earth is so much more massive
(b) the earth because the satellite has so little mass
(c) Earth and the satellite feel exactly the same force.
(d) It depends on the distance of the satellite from Earth.
33. You are in a train traveling on a horizontal track and notice that a piece of luggage starts to slide directly
toward the front of the train. From this observation, you can conclude that this train is
(a) speeding up.
(d) speeding up and changing direction.
(b) slowing down.
(e) slowing down and changing direction.
(c) changing direction.
34. A crate is sliding down an inclined ramp at a constant speed of 0.55 m/s. The vector sum of all the
forces acting on this crate must point
(a) down the ramp.
(d) vertically downward.
(b) up the ramp.
(e) None of the above choices is correct.
(c) perpendicular to the ramp.
35. Bill and his daughter Susan are both standing on identical skateboards (with really good frictionless ball
bearings), initially at rest. Bill weighs three times as much as Susan. Bill pushes horizontally on Susan's
back, causing Susan to start moving away from Bill. Just after Bill stops pushing,
(a) Susan and Bill are moving away from each other, and Susan's speed is three times that of Bill.
(b) Susan is moving away from Bill, and Bill is stationary.
(c) Susan and Bill are moving away from each other, with equal speeds.
(d) Susan and Bill are moving away from each other, and Susan's speed is one-third that of Bill.
36. An object is moving with constant non-zero velocity. Which of the following statements about it must be
true?
(a) A constant force is being applied to it in the direction of motion.
(b) A constant force is being applied to it in the direction opposite of motion.
(c) A constant force is being applied to it perpendicular to the direction of motion.
(d) The net force on the object is zero.
(e) Its acceleration is in the same direction as it velocity.
37. Two objects have masses m and 5m, respectively. They both are placed side by side on a frictionless
inclined ramp and allowed to slide down from rest without any air resistance. Which one of the
following statements about these objects is correct?
(a) It takes the lighter object 5 times longer to reach the bottom of the ramp than the heavier.
(b) It takes the lighter object 10 times longer to reach the bottom of the ramp than the heavier.
(c) It takes the heavier object 5 times longer to reach the bottom of the ramp than the lighter.
(d) It takes the heavier object 10 times longer to reach the bottom of the ramp than the lighter.
(e) The two objects reach the bottom of the ramp at exactly the same time.
38. A block of mass m sits at rest on a rough inclined ramp that makes an angle θ with the horizontal. What
must be true about force of static friction f on the block?
(a) f > mg
(c) f > mg sin θ
(e) f = mg sin θ
(b) f > mg cos θ
(d) f = mg cos θ
39. A block of mass m sits at rest on a rough inclined ramp that makes an angle θ with the horizontal. What
must be true about normal force F on the block due to the ramp?
(a) F > mg
(c) F > mg sin θ
(e) F = mg sin θ
(b) F > mg cos θ
(d) F = mg cos θ
40. The figure shows an acceleration-versus-force graph for a 125-g object. What should be the value of the
first tick-mark on the vertical scale, as indicated by the arrow in the figure?
(a) 4
(b) 8
(c) 0.00400
(d) 0.00800
41. The figure shows an object's acceleration-versus-force graph. What is the mass of this object?
(a) 2.5 g
(b) 1.6 g
(c) 630 g
(d) 400,000 g
42. In the figure, block A has a mass of 3.00 kg. It rests on a smooth horizontal table and is connected by a
very light horizontal string over an ideal pulley to block B, which has a mass of 2.00 kg. When block B
is gently released from rest, how long does it take block B to travel 80.0 cm?
(a) 0.404 s
(b) 0.494 s
(c) 0.639 s
(d) 0.785 s
(e) 0.935 s
Circular
43. You are making a circular turn in your car on a horizontal road when you hit a big patch of ice, causing
the force of friction between the tires and the road to become zero. While the car is on the ice, it
(a) moves along a straight-line path away from the center of the circle.
(b) moves along a straight-line path toward the center of the circle.
(c) moves along a straight-line path in its original direction.
(d) continues to follow a circular path, but with a radius larger than the original radius.
(e) moves along a path that is neither straight nor circular.
44. Two small balls, A and B, attract each other gravitationally with a force of magnitude F. If we now
double both masses and the separation of the balls, what will now be the magnitude of the attractive
force on each one?
(a) 16F
(b) 8F
(c) 4F
(d) F
(e) F/4
45. A spaceship is traveling to the Moon. At what point is it beyond the pull of Earth's gravity?
(a) when it gets above the atmosphere
(b) when it is half-way there
(c) when it is closer to the Moon than it is to Earth
(d) It is never beyond the pull of Earth's gravity.
46. If you stood on a planet having a mass four times that of Earth's mass, and a radius two times that of
Earth's radius, you would weigh
(a) the same as you do on Earth.
(c) two times less than you do on Earth.
(b) two times more than you do on Earth.
(d) four times more than you do on Earth.
47. An piece of space debris is released from rest at an altitude that is two earth radii from the center of the
earth. Compared to its weight on Earth, the weight of this debris is
(a) zero.
(b) the same as on the surface of the earth.
(c) one-half of its weight on the surface of the earth.
(d) one-third of its weight on the surface of the earth.
(e) one-quarter of its weight on the surface of the earth.
48. A satellite encircles Mars at a distance above its surface equal to 3 times the radius of Mars. If gm is the
acceleration due to gravity at the surface of Mars, what is the acceleration due to gravity at the location
of the satellite?
(a) gm/9
(b) 0
(d) gm/3
(e) gm/16
(c) gm
49. A hypothetical planet has a mass of one-half that of the earth and a radius of twice that of the earth.
What is the acceleration due to gravity on the planet in terms of g, the acceleration due to gravity at the
surface of the earth?
(a) g
(b) g/2
(c) g/4
(d) g/8
(e) g/16
50. Two planets have the same surface gravity, but planet B has twice the radius of planet A. If planet A
has mass m, what is the mass of planet B?
(b) m
(d) 4m
(e) m/4
(a) m/
(c) m
51. Two planets have the same surface gravity, but planet B has twice the mass of planet A. If planet A has
radius r, what is the radius of planet B?
(b) r
(d) 4r
(e) 2r
(a) r/
(c) r
52. Satellite A has twice the mass of satellite B, and moves at the same orbital distance from Earth as
satellite B. Compare the speeds of the two satellites.
(a) The speed of B is twice the speed of A.
(d) The speed of B is equal to the speed of A.
(b) The speed of B is one-half the speed of A.
(e) The speed of B is four times the speed of A.
(c) The speed of B is one-fourth the speed of A.
53. A particularly scary roller coaster contains a loop-the-loop in which the car and rider are completely
upside down. If the radius of the loop is
with what minimum speed must the car traverse the loop
so that the rider does not fall out while upside down at the top? Assume the rider is not strapped to the
car.
(a) 11.4 m/s
(b) 12.5 m/s
(c) 10.1 m/s
(d) 14.9 m/s
54. A 20-g bead is attached to a light 120-cm-long string as shown in the figure. This bead moves in a
horizontal circle with a constant speed of 1.5 m/s. What is the tension in the string if the angle α is
measured to be 25°?
(a) 0.089 N
(b) 0.041 N
(c) 0.20 N
(d) 0.22 N
(e) 0.46 N
55. A 20-g bead is attached to a light 120 cm-long string as shown in the figure. If the angle α is measured
to be 18°, what is the speed of the mass?
(a) 0.55 m/s
(b) 2.0 m/s
(c) 3.8 m/s
(d) 1.3 m/s
(e) 1.1 m/s
56. Two horizontal curves on a bobsled run are banked at the same angle, but one has twice the radius of the
other. The safe speed (for which no friction is needed to stay on the run) for the smaller radius curve is
v. What is the safe speed on the larger-radius curve?
(b) 2v
(d) v/2
(a) v /
(c) v
Energy
57. If the force on an object is in the negative direction, the work it does on the object must be
(a) negative.
(b) positive.
(c) The work could be either positive or negative, depending on the direction the object moves.
58. A 4.0 kg object is moving with speed 2.0 m/s. A 1.0 kg object is moving with speed 4.0 m/s. Both
objects encounter the same constant braking force, and are brought to rest. Which object travels the
greater distance before stopping?
(a) the 4.0 kg object
(d) It cannot be determined from the
(b) the 1.0 kg object
information given.
(c) Both objects travel the same distance.
59. You slam on the brakes of your car in a panic, and skid a certain distance on a straight level road. If you
had been traveling twice as fast, what distance would the car have skidded, under the same conditions?
(a) It would have skidded 4 times farther.
(b) It would have skidded twice as far.
(c) It would have skidded 1.4 times farther.
(d) It would have skidded one half as far.
(e) It is impossible to tell from the information given.
60. (II) The force on a particle, acting along the x axis, varies as shown in Fig. 6–38. Determine the work
done by this force to move the particle along the x axis: (a) from x = 0.0 to x = 10.0 m; (b) from x = 0.0
to x = 15.0 m.