AP Physics C: Mechanics 2026 Practice Exam 1 - 40
Multiple-Choice Questions with Verified Answer Key, Detailed
Solutions & Calculations. - 84 Questions and Answers Already
Graded A+ Premium Exam Tested And Verified
Subject Area Physics
Description This exam covers calculus-based mechanics topics including kinematics,
dynamics, work and energy, momentum, rotational motion, oscillations, and
gravitation. Students are expected to apply fundamental principles to complex
problems requiring multi-step reasoning and mathematical analysis.
Expected Grade 5 (A+ equivalent)
Total Questions 84
Duration 1 hour 30 minutes (multiple-choice section)
Learning Outcomes 1. Apply Newton's laws to systems with multiple forces and accelerations
2. Use conservation laws to solve problems in mechanics
3. Analyze rotational motion using torque and angular momentum
4. Solve problems involving simple harmonic motion and gravitation
Accreditation Meets College Board standards for AP Physics C: Mechanics
Page 1
,1. A particle moves along the x-axis with acceleration a(t) = 6t - 4 m/s². At t =
0, its velocity is 5 m/s and its position is 2 m. What is its position at t = 3 s?
Answer: 26 m
Integrate acceleration to get velocity: v(t)=(6t-4)dt = 3t²-4t+5. Integrate again:
x(t)=v dt = t³-2t²+5t+2. At t=3, x=27-18+15+2=26 m.
2. Two blocks of equal mass 5 kg are connected by a light string over a
frictionless pulley. One block rests on a horizontal surface with coefficient of
kinetic friction 0.2, the other hangs freely. The system is released from rest.
What is the tension in the string? (g = 10 m/s²)
Answer: 30 N
For the hanging block: mg - T = ma. For the block on the table: T - mg = ma.
Solve: a = (mg - mg)/(2m) = (10-2)/2 = 4 m/s². Then T = m(g-a) = 5(10-4) = 30 N.
3. A spring of force constant 500 N/m is compressed by 0.1 m. A 2 kg block is
placed against it and released on a horizontal surface with coefficient of kinetic
friction 0.3. What is the maximum speed of the block after release? (g = 10
m/s²)
Answer: 1.4 m/s
Initial spring energy = ½(500)(0.1)² = 2.5 J. Work done by friction over
compression distance = mg(0.1) = 0.3(2)(10)(0.1) = 0.6 J. Remaining KE = 1.9 J,
so v = (2(1.9)/2) = 1.9 1.38 m/s, rounding to 1.4 m/s.
4. Particle A of mass m moves with velocity v in the +x direction. Particle B of
mass 2m moves with velocity v in the +y direction. They collide and stick
together. What is the speed of the combined mass after collision?
Answer: v5/3
Momentum conservation: x: mv = 3m V_x -> V_x = v/3; y: 2mv = 3m V_y -> V_y
= 2v/3. Speed = ((v/3)² + (2v/3)²) = v5/3.
Page 2
, 5. A disk rotates with constant angular acceleration = -3 rad/s². At t=0,
angular velocity is 12 rad/s. What is the angular displacement when the
angular velocity becomes -6 rad/s?
Answer: 18 rad
Use ² = ² + 2. = (² - ²)/(2) = (36 - 144)/(2(-3)) = (-108)/(-6) = 18 rad.
6. A uniform rod of length L and mass M is hinged at one end and released
from a horizontal position. What is the initial angular acceleration? (I_end =
ML²/3)
Answer: 3g/(2L)
Torque due to gravity: = Mg(L/2). Moment of inertia about end: I = ML²/3. = /I
= (MgL/2)/(ML²/3) = 3g/(2L).
7. A particle of mass m moves in a circle of radius R with speed v on a
frictionless table, attached to a string passing through a hole. The string is
pulled slowly to reduce the radius to R/2. What is the final speed of the
particle?
Answer: 2v
Angular momentum about the hole is conserved: L_i = mvR, L_f = mv_f(R/2).
Equating gives v_f = 2v.
8. A mass-spring system oscillates with amplitude A. At t=0, the displacement
is A/2 and the velocity is positive. The phase constant (in rad) is:
Answer: -/3
x = A cos = A/2 -> cos = 1/2 -> = ±/3. v = -A sin > 0 -> sin < 0, so = -/3.
9. Satellite A orbits Earth at radius R with period T. Satellite B has twice the
mass and orbits at radius 2R. What is the ratio of their periods T_B/T_A?
Answer: 22
Kepler's third law: T R^(3/2). T_B/T_A = (2R/R)^(3/2) = 2^(3/2) = 22.
Page 3
Multiple-Choice Questions with Verified Answer Key, Detailed
Solutions & Calculations. - 84 Questions and Answers Already
Graded A+ Premium Exam Tested And Verified
Subject Area Physics
Description This exam covers calculus-based mechanics topics including kinematics,
dynamics, work and energy, momentum, rotational motion, oscillations, and
gravitation. Students are expected to apply fundamental principles to complex
problems requiring multi-step reasoning and mathematical analysis.
Expected Grade 5 (A+ equivalent)
Total Questions 84
Duration 1 hour 30 minutes (multiple-choice section)
Learning Outcomes 1. Apply Newton's laws to systems with multiple forces and accelerations
2. Use conservation laws to solve problems in mechanics
3. Analyze rotational motion using torque and angular momentum
4. Solve problems involving simple harmonic motion and gravitation
Accreditation Meets College Board standards for AP Physics C: Mechanics
Page 1
,1. A particle moves along the x-axis with acceleration a(t) = 6t - 4 m/s². At t =
0, its velocity is 5 m/s and its position is 2 m. What is its position at t = 3 s?
Answer: 26 m
Integrate acceleration to get velocity: v(t)=(6t-4)dt = 3t²-4t+5. Integrate again:
x(t)=v dt = t³-2t²+5t+2. At t=3, x=27-18+15+2=26 m.
2. Two blocks of equal mass 5 kg are connected by a light string over a
frictionless pulley. One block rests on a horizontal surface with coefficient of
kinetic friction 0.2, the other hangs freely. The system is released from rest.
What is the tension in the string? (g = 10 m/s²)
Answer: 30 N
For the hanging block: mg - T = ma. For the block on the table: T - mg = ma.
Solve: a = (mg - mg)/(2m) = (10-2)/2 = 4 m/s². Then T = m(g-a) = 5(10-4) = 30 N.
3. A spring of force constant 500 N/m is compressed by 0.1 m. A 2 kg block is
placed against it and released on a horizontal surface with coefficient of kinetic
friction 0.3. What is the maximum speed of the block after release? (g = 10
m/s²)
Answer: 1.4 m/s
Initial spring energy = ½(500)(0.1)² = 2.5 J. Work done by friction over
compression distance = mg(0.1) = 0.3(2)(10)(0.1) = 0.6 J. Remaining KE = 1.9 J,
so v = (2(1.9)/2) = 1.9 1.38 m/s, rounding to 1.4 m/s.
4. Particle A of mass m moves with velocity v in the +x direction. Particle B of
mass 2m moves with velocity v in the +y direction. They collide and stick
together. What is the speed of the combined mass after collision?
Answer: v5/3
Momentum conservation: x: mv = 3m V_x -> V_x = v/3; y: 2mv = 3m V_y -> V_y
= 2v/3. Speed = ((v/3)² + (2v/3)²) = v5/3.
Page 2
, 5. A disk rotates with constant angular acceleration = -3 rad/s². At t=0,
angular velocity is 12 rad/s. What is the angular displacement when the
angular velocity becomes -6 rad/s?
Answer: 18 rad
Use ² = ² + 2. = (² - ²)/(2) = (36 - 144)/(2(-3)) = (-108)/(-6) = 18 rad.
6. A uniform rod of length L and mass M is hinged at one end and released
from a horizontal position. What is the initial angular acceleration? (I_end =
ML²/3)
Answer: 3g/(2L)
Torque due to gravity: = Mg(L/2). Moment of inertia about end: I = ML²/3. = /I
= (MgL/2)/(ML²/3) = 3g/(2L).
7. A particle of mass m moves in a circle of radius R with speed v on a
frictionless table, attached to a string passing through a hole. The string is
pulled slowly to reduce the radius to R/2. What is the final speed of the
particle?
Answer: 2v
Angular momentum about the hole is conserved: L_i = mvR, L_f = mv_f(R/2).
Equating gives v_f = 2v.
8. A mass-spring system oscillates with amplitude A. At t=0, the displacement
is A/2 and the velocity is positive. The phase constant (in rad) is:
Answer: -/3
x = A cos = A/2 -> cos = 1/2 -> = ±/3. v = -A sin > 0 -> sin < 0, so = -/3.
9. Satellite A orbits Earth at radius R with period T. Satellite B has twice the
mass and orbits at radius 2R. What is the ratio of their periods T_B/T_A?
Answer: 22
Kepler's third law: T R^(3/2). T_B/T_A = (2R/R)^(3/2) = 2^(3/2) = 22.
Page 3
