AP Physics C Review Packet 1st Semester
Problem: Acceleration (CM-1993)
Displacement (x, y or z)
Change in position.
Depends only on initial and final positions, not
on path.
Includes direction.
x = vdt
1.
Velocity (v)
Displacement per unit time
Average velocity
vave = ∆x/∆t
Instantaneous velocity
v = dx/dt
v = adt
In the absence of air friction, an object dropped
near the surface of the Earth experiences a
constant acceleration of about 9.8 m/s2. This
means that the
(A) speed of the object increases 9.8 m/s during
each second
(B) (B) speed of the object as it falls is 9.8 m/s
(C) object falls 9.8 meters during each second
(D) object falls 9.8 meters during the first second
only
(E) derivative of the distance with respect to time
for the object equals 9.8 m/s2
Justify your answer:
Acceleration (a)
A change in velocity: speeding up, slowing down, or
turning.
Average acceleration
aave = ∆v/∆t
Instantaneous acceleration
a = dv/dt
Problem: Acceleration (CM-1988)
Problem: Acceleration (B-1993)
11. A particle moves along the x-axis with a nonconstant acceleration described by a = 12t, where
a is in meters per second squared and t is in
seconds. If the particle starts from rest so that
its speed v and position x are zero when t = 0,
where is it located when t = 2 seconds?
(A) x = 12 m
(B) (B) x = 16m
(C) (C) x = 24 m
(D) (D) x = 32 m
(E) (E) x = 48 m
1. In which of the following situations would an
object be accelerated?
I. It moves in a straight line at constant speed.
II. It moves with uniform circular motion.
III. It travels as a projectile in a gravitational field
with negligible air resistance.
(A) I only
(B) III only
(C) I and II only
(D) II and III only
(E) I, II, and III
Show your work:
State your reasoning:
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AP Physics C Review Packet 1st Semester
Kinematic Equations
Use these only in situations of constant, or uniform,
acceleration. (Otherwise, you need to do derivatives
and integrals!)
v = vo + at
x = xo + vot + 1/2 at2
v2 = vo2 + 2a(∆x)
Problem: General Kinematics (CM-1988)
Questions 14-15: An object moving in a straight line
has a velocity v in meters per second that varies with
time t in seconds according to the following function.
v = 4 + 0.5 t2
14. The instantaneous acceleration of the object at t
= 2 seconds is
(A) 2 m/s2 (B) 4 m/s2
(C) 5 m/s2
(D)
6 m/s2
(E) 8 m/s2
Problem: Kinematic Equations (B-1984)
65. A body moving in the positive x direction passes
the origin at time t = 0. Between t = 0 and t = 1
second, the body has a constant speed of 24
meters per second. At t = 1 second, the body is
given a constant acceleration of 6 meters per
second squared in the negative x direction. The
position x of the body at t = 11 seconds is
(A) +99 m
(B) +36 m
(C) -36 m
(D) -75 m
(E) -99 m
Show your work:
15. The displacement of the object between t = 0 and
t = 6 seconds is
(A) 22 m
(B) 28 m
(C) 40 m
(D) 42
m
(E) 60 m
Show your work:
Show your work:
Problem: Kinematic Equations (CM-1988)
Problem: Kinematic Equations (CM-1993)
2.
A 500-kilogram sports car accelerates uniformly
from rest, reaching a speed of 30 meters per
second in 6 seconds. During the 6 seconds, the
car has traveled a distance of
(A) 15 m
(B) 30 m
(C) 60 m
(D) 90
m
(E) 180 m
5.
Show your work:
An object released from rest at time t = 0 slides
down a frictionless incline a distance of 1 meter
during the first second. The distance traveled by
the object during the time interval from t = 1
second to t = 2 seconds is
(A) 1 m (B) 2 m (C) 3 m
(D) 4m (E) 5 m
Show your work:
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AP Physics C Review Packet 1st Semester
Kinematic graphs
Slope of line of time-domain graph
Equivalent to graphical derivative
Use to go from displacement to velocity
Use to go from velocity to acceleration
Area under curve of time-domain graph
Equivalent to graphical integral
Use to go from velocity to displacement
Use to go from acceleration to velocity
Problem: Kinematic Graphs (CM-1998)
3. The graph above shows the velocity v as a
function of time t for an object moving in a
straight line. Which of the following graphs
shows the corresponding displacement x as a
function of time t for the same time interval?
Problem: Kinematic Graphs (CM-1988)
Explain your answer:
D is the answer!
Problem: Kinematic Graphs (B-1984)
3.
The graph shows the velocity versus time for an
object moving in a straight line. At what time
after time = 0 does the abject again pass through
its initial position?
(A)
(B)
(C)
(D)
(E)
Between O and 1 s
1s
Between 1 and 2 s
2s
Between 2 and 3 s
Explain your answer:
Explain your answer:
E is the answer!!
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AP Physics C Review Packet 1st Semester
Free Fall
Occurs when an object falls unimpeded.
Gravity accelerates the object toward the earth.
g = 9.8 m/s2 downward.
a = -g if up is positive.
acceleration is down when ball is thrown up
EVERYWHERE in the balls flight.
Vectors have both magnitude and direction
displacement, velocity, acceleration
Scalars have magnitude only
distance, speed, time, mass
Unit vectors
Specify direction only.
Used to represent a vector in terms of components.
a = axi + ayj + azk
Problem: Free Fall (B-1993)
5. An object is released from rest on a planet that has
no atmosphere. The object falls freely for 3.0 meters
in the first second. What is the magnitude of the
acceleration due to gravity on the planet?
(A) l .5 m/s2
(B) 3.0 m/s2
(C) 6.0 m/s2
(D) 10.0 m/s2
(E) 12.0 m/s2
Multiplication of Vector by Scalar
Physics application
Momentum:
p = mv
Electric force:
F = qE
Result
A vector with the same direction, a different
magnitude and perhaps different units.
Multiplication of Vector by Vector (Dot Product)
C = AB cos 
C = AxBx + AyBy + AzBz
Physics application
Work:
W=Fd
Result
A scalar with magnitude and no direction.
Show your work:
Multiplication of Vector by Vector (Cross Product)
C=AB
C = AB sin  (magnitude)
Physics application
Work
=rF
Magnetic force
F = qv  B
Result
A vector with magnitude and a direction
perpendicular to the plane established by the
other two vectors.
Problem: Free Fall (CM-1993)
19. An object is shot vertically upward into the air
with a positive initial velocity. Which of the
following correctly describes the velocity and
acceleration of the object at its maximum
elevation?
Velocity
Acceleration
(A) Positive
Positive
(B) Zero
Zero
(C) Negative
Negative
(D) Zero
Negative
(E) Positive
Negative
Kinematic Equations (in 3 dimensions)
v = vo + at
r = ro + vot + ½ a t2
v  v = vo  vo + 2ar
Projectile Motion
Horizontal velocity is constant.
x = vo,xt
Vertical velocity is accelerated at -g.
vy = vo - gt
y = yo + Vo,yt - 1/2gt2
vy2 = vo,y2 - 2g(y – yo)
The trajectory is defined mathematically by a
parabola.
Explain your reasoning:
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AP Physics C Review Packet 1st Semester
Problem: Projectile (CM-1998)
Problem: Projectile (CM-1993)
2. The velocity of a projectile at launch has a horizontal component vh and a vertical component vv. Air
resistance is negligible. When the projectile is at the
highest point of its trajectory, which of the following
show the vertical and horizontal components of its
velocity and the vertical component of its
acceleration?
Vertical
Horizontal
Vertical
Velocity
Velocity
Acceleration
(A)
vv
vh
0
(B)
vv
0
0
(C)
0
vh
0
(D
0
0
g
(E)
0
vh
g
A ball is thrown and follows a parabolic path, as
shown above. Air friction is negligible. Point Q is the
highest point on the path.
27. Which of the following best indicates the
direction of the acceleration, if any, of the ball at
point Q ?
(A)
(B)
(C)
(D)
Justify your answer:
(E) There is no acceleration of the ball at point Q.
Justify your answer:
Problem: Projectile (CM-1998)
Problem: Projectile (CM-1988)
10. A projectile is fired from the surface of the Earth
with a speed of 200 meters per second at an
angle of 30° above the horizontal. If the ground
is level, what is the maximum height reached by
the projectile?
(A) 5 m (B) 10 m
(C) 500 m
(D) 1,000 m (E) 2,000 m
26. A target T lies flat on the ground 3 m from the
side of a building that is 10 m tall, as shown
above. A student rolls a ball off the horizontal
roof of the building in the direction of the target.
Air resistance is negligible. The horizontal speed
with which the ball must leave the roof if it is to
strike the target is most nearly
(A) 3/10 m/s
(B) 2 m/s
3
m/s
(D) 3 m/s
2
5
(E) 10
m/s
3
Show your work:
Show your work:
(C)
Uniform Circular Motion
Object moves in a circle without changing speed.
The object’s velocity is continually changing.
Therefore, the object must be accelerating.
The acceleration vector is pointed toward the center
of the circle in which the object is moving.
This acceleration is referred to as centripetal
acceleration.
Acceleration in Uniform Circular Motion
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AP Physics C Review Packet 1st Semester
Centripetal acceleration.
Perpendicular to the velocity.
Does not change an object’s speed.
ac = v2/r
v: velocity
r: radius of rotation
average acceleration of the object between time
t1 and t2 was
(A) zero
(B) directed north
(C) directed west (D) directed north of east
(E) directed north of west
Justify your answer:
Problem: Uniform Circular Motion (CM1998)
Relative Motion
Usually requires vector addition.
You may make any observer the “stationary”
observer.
25. A figure of a dancer on a music box moves counterclockwise at constant speed around the path
shown above. The path is such that the lengths of
its segments, PQ, QR, RS, and SP, are equal.
Arcs QR and SP are semicircles. Which of the
following best represents the magnitude of the
dancer's acceleration as a function of time t
during one trip around the path, beginning at
point P ?
Problem: Relative Motion (CM-1993)
3.
At a particular instant, a stationary observer on
the ground sees a package falling with speed v1
at an angle to the vertical. To a pilot flying
horizontally at constant speed relative to the
ground, the package appears to be falling
vertically with a speed v2 at that instant. What is
the speed of the pilot relative to the ground?
(A) v1 + v2
(C) v2-v1
(B) v1 - v2
(D) v 1 2  v 2 2
(E) v 1 2  v 2 2
Show your work:
Justify your answer:
B is the answer!
Problem: Centripetal Acceleration (CM1988)
7. Vectors V1, and V2 shown above have equal
magnitudes. The vectors represent the velocities
of an object at times t1, and t2, respectively. The
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AP Physics C Review Packet 1st Semester
The acceleration is proportional to the net (or
resultant) force and is in the direction that the net
force acts.
This law is commonly applied to the vertical
component of velocity.
F = ma (Unit of force is the Newton)
Problem: Relative Motion (CM-1988)
6. Two people are in a boat that is capable of a
maximum speed of 5 kilometers per hour in still
water, and wish to cross a river 1 kilometer wide to a
point directly across from their starting point. If the
speed of the water in the river is 5 kilometers per
hour, how much time is required for the crossing?
(A) 0.05 hr
(B) 0.1 hr (C) 1 hr
(D) 10 hr
(E) The point directly across from the starting point
cannot be reached under these conditions.
Some 2nd law problems require a force to be
distributed to several masses undergoing the same
acceleration.
Show your work:
Problem: 2nd Law (CM-1984)
9. When the frictionless system shown above is
accelerated by an applied force of magnitude F, the tension
in the string between the blocks is
(A) 2 F
(B) F
(C) (2/3)F
(D) 0.5F
(E) (1/3)F
Force
A push or pull on an object.
A vector
Unbalanced forces cause an object to accelerate…
To speed up
To slow down
To change direction
Show your work:
Types of Forces
Contact forces: involve contact between bodies.
Field forces: act without necessity of contact.
Gravitational
Electromagnetic
Weak Nuclear
Strong Nuclear
Newton’s Third Law
For every action there exists an equal and opposite
reaction.
If A exerts a force F on B, then B exerts a force of -F
on A.
Problem: Newton’s 3rd Law (CM-1993)
Forces and Equilibrium
If the net force on a body is zero, it is in equilibrium.
An object in equilibrium may be moving relative to
us (dynamic equilibrium).
An object in equilibrium may appear to be at rest (
static equilibrium).
5. If F1 is the magnitude of the force exerted by the
Earth on a satellite in orbit about the Earth and F2 is
the magnitude of the force exerted by the satellite on
the Earth, then which of the following is true?
(A) F1 is much greater than F2.
(B) F1 is slightly greater than F2.
(C) F1 is equal to F2.
(D) F2 is slightly greater than F1
(E) F2 is much greater than F1
Newton’s First Law
The Law of Inertia.
A body in motion stays in motion in a straight line
unless acted upon by an external force.
This law is commonly applied to the horizontal
component of velocity, which is assumed not to
change during the flight of a projectile.
Justify your answer:
Inertia
Inertia, or the resistance of an object to being
accelerated, is the same thing as mass to a
physicist.
Newton’s Second Law
A body accelerates when acted upon by a net external
force.
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AP Physics C Review Packet 1st Semester
Tension is determined by focusing on one block and
ignoring the rest of the world.
Weight
Force due to gravitation attraction.
W = mg
Normal force
Contact force that keeps one object from invading
another object.
Normal force on flat surface is usually
N = mg
Normal force on ramp is usually
N = mg cos 

Tension
A pulling force.
Arises at the molecular level, when a rope, string, or
cable resists being pulled apart.
Problem: 2nd Law and Pulleys (CM-1993)
9 Two 0.60-kilogram objects are connected by a thread
that passes over a light, frictionless pulley, as shown
above. The objects are initially held at rest. If a third
object with a mass of 0.30 kilogram is added on top of
one of the 0.60-kilogram objects as shown and the objects
are released, the magnitude of the acceleration of the
0.30-kilogram object is most nearly
(A) 10.0 m/s2
(B) 6.0 m/s2
(C) 3.0 m/s2
2
2
(D) 2.0 m/s
(E) 1.0 m/s
Tension (static problems)
Net horizontal and vertical forces are equal to zero if
the system is not accelerating.
Tension (dynamic problems)
Net force is zero if no acceleration.
Tension can increase or decrease
acceleration occurs.
Show your work:
as
Problem: Tension in dynamic problem
(CM-1998)
Friction
A force that opposes sliding motion.
Always parallel to surfaces.
Static friction
Exists before sliding occurs.
Prevents sliding
Can increase up to some maximum value
fs  sN
Kinetic friction
Exists after sliding occurs.
Produces heat; dissipates energy.
Is constant proportional to the normal force.
fk = kN
19. A descending elevator of mass 1,000 kg is uniformly decelerated to rest over a distance of 8 m
by a cable in which the tension is 11,000 N. The
speed vi of the elevator at the beginning of the 8
m descent is most nearly
(A) 4 m/s
(B) 10 m/s
(C) 13 m/s
(D) 16 m/s
(E) 21 m/s
Show your work:
Pulley problems
Magic pulleys simply bend the coordinate system.
Acceleration is determined first by considering entire
system (all of the mass!)
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AP Physics C Review Packet 1st Semester
Problem: Newton’s 2nd Law and Friction
(CM-1993)
Problem: Non-constant force (CM-1984)
7.
34. A block of mass 5 kilograms lies on an inclined
plane, as shown above. The horizontal and
vertical supports for the plane have lengths of 4
meters and 3 meters, respectively. The
coefficient of friction between the plane and the
block is 0.3. The magnitude of the force F
necessary to pull the block up the plane with
constant speed is most nearly
(A) 30 N
(B) 42 N
(C) 49 N
(D) 50 N
(E) 58 N
The parabola above is a graph of speed v as a
function of time t for an object. Which of the
following graphs best represents the magnitude F
of the net force exerted on the object as a
function of time t ?
(A) F
(B) F
Show your work:
Justify your answer:
E is the answer!!
Problem: Time-dependent force (CM-1988)
4.
A particle of mass m moves along a straight path
with a speed v defined by the function v = bt2 +
c, where b and c are constants and t is time.
What is the magnitude F of the net force on the
particle at time t = t1 ?
(A) bt1 2 + c
(B) 3mbt1 + 2c
(C) mbt1
(D) mbt1 + c
(E) 2mbt1
Drag Force
Slows an object down as it passes through a fluid.
Acts in opposite direction to velocity.
Imposes a terminal velocity.
fD = bv + cv2
b and c depend upon
shape and size of object
properties of fluid
b is important at low velocity
c is important at high velocity
Show your work:
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AP Physics C Review Packet 1st Semester
Kinetic Energy (K)
A form of mechanical energy
Energy due to motion
K = ½ m v2
Problem: Drag force (CM-1998)
34. An object is released from rest at time t = 0 and
falls through the air, which exerts a resistive
force such that the acceleration a of the object is
given by a = g - bv, where v is the object's speed
and b is a constant. If limiting cases for large
and small values of t are considered, which of
the following is a possible expression for the
speed of the object as an explicit function of
time?
(A) v = g(1 - e-bt)/b
(B) V = (geht)/b
(C)
2
v = gt - bt
(D) v = (g + a)t/b
(E) v =
v0+ gt, v0  O
Problem: Kinetic Energy (CM 1993)
6. A ball is thrown upward. At a height of 10 meters
above the ground, the ball has a potential energy of
50 joules (with the potential energy equal to zero at
ground level) and is moving upward with a kinetic
energy of 50 joules. Air friction is negligible. The
maximum height reached by the ball is most nearly
(A) 10 m
(B) 20 m
(C) 30 m
(D) 40
m
(E) 50 m
Show your work:
Show your work:
Work
A force does work on a body when it causes a
displacement.
There is no work done by a force if it causes no
displacement.
Forces perpendicular to displacement, such as the
normal force, can do no work.
For example, centripetal forces never do work.
Net Work
Net work (Wnet) is the sum of the work done on an
object by all forces acting upon the object.
Calculating Work
W = F • s = F s cos 
W =  F(x) dx
W =  F • ds
SI Unit: Joule (N m)
The area under the curve of a graph of force vs
displacement gives the work done by the force.
The Work-Energy Theorem
Wnet = KE
When net work due to all forces acting upon an
object is positive, the kinetic energy of the object
will increase.
When net work due to all forces acting upon an
object is negative, the kinetic energy of the object
will decrease.
When there is no net work acting upon an object, the
kinetic energy of the object will be unchanged.
Wnet = W
Problem: Work (CM 1993)
14. A weight lifter lifts a mass m at constant speed to
a height h in time t. How much work is done by
the weight lifter?
(A) mg
(B) mh
(C) mgh
(D) mght
(E) mgh/t
Show your work:
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AP Physics C Review Packet 1st Semester
Power (P)
The rate at which work is done.
Pave = W / t
P = dW/dt
P=F•v
SI Unit of Power: Watt = J/s
British Unit of Power: horsepower
1 hp = 746 Watts
Problem: Work-Energy Theorem (CM
1984)
15. The following graphs, all drawn to the same
scale, represent the net force F as a function of
displacement x for an object that moves along a
straight line. Which graph represents the force that
will cause the greatest change in the kinetic energy of
the object from x = 0 to x = x1?
Problem: Power (CM 1984)
8. An object of mass m is lifted at constant velocity
a vertical distance H in time T. The power supplied
by the lifting force is
(A) mgHT
(B) mgH/T
(C) mg/HT
(D)
mgT/H
(E) zero
Show your work:
State your reasoning:
E is the answer!
Problem: Power (CM 1993)
Problem: Work-Energy Theorem (CM
1988)
Show your work:
10. During a certain time interval, a constant force
delivers an average power of 4 watts to an object. If
the object has an average speed of 2 meters per
second and the force acts in the direction of motion
of the object, the magnitude of the force is
(A) 16 N
(B) 8 N
(C) 6 N
(D) 4N
(E) 2N
17. A rock is lifted for a certain time by a force F
that is greater in magnitude than the rock's
weight W. The change in kinetic energy of the
rock during this time is equal to the
(A) work done by the net force (F - W)
(B) work done by F alone
(C) work done by W alone
(D) difference in the momentum of the rock
before and after this time
(E) difference in the potential energy of the rock
before and after this time.
Force types
Conservative forces:
Work in moving an object is path independent.
Work in moving an object along a closed path is zero.
Work is equal to negative change in potential energy.
Ex: gravity, electrostatic, magnetostatic, springs
State your reasoning:
Non-conservative forces:
Work is path dependent.
Work along a closed path is NOT zero.
Work is related to a change in total energy (including
thermal energy).
Ex: friction, drag, magnetodynamic
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