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Prepare for the timed AP Physics C: Mechanics test.

Your answers are held until submission. The final review identifies the units that need another pass.

AP Physics C: Mechanics coverage and review map

Connect every question to the exact skill it rehearses. Work through the units in order, then return to any topic that still needs a hint or a second attempt.

01

Kinematics

Vector motion and calculus

Goal: recognise a kinematics problem from its wording, carry out the governing method, and check that the result is reasonable.

02

Force and Translational Dynamics

Newton's laws and differential models

Goal: recognise a force and translational dynamics problem from its wording, carry out the governing method, and check that the result is reasonable.

03

Work, Energy, and Power

Line integrals and energy

Goal: recognise a work, energy, and power problem from its wording, carry out the governing method, and check that the result is reasonable.

04

Linear Momentum

Systems, impulse, collisions

Goal: recognise a linear momentum problem from its wording, carry out the governing method, and check that the result is reasonable.

05

Torque and Rotational Dynamics

Rigid-body rotation

Goal: recognise a torque and rotational dynamics problem from its wording, carry out the governing method, and check that the result is reasonable.

06

Energy and Momentum of Rotating Systems

Angular conservation

Goal: recognise a energy and momentum of rotating systems problem from its wording, carry out the governing method, and check that the result is reasonable.

07

Oscillations

Differential equations and SHM

Goal: recognise a oscillations problem from its wording, carry out the governing method, and check that the result is reasonable.

AP Physics C: Mechanics questions with worked answers

These 8 questions are printed in full on this page and are drawn across all 7 course units. Nothing here is generated on the fly. Cover the options, solve each one on paper, and only then open the worked answer to compare your method with the one shown.

Question 1: A particle has position x(t) = 4t^3 - 2t^2 meters. What are its velocity and acceleration at t = 2 s?

AP Physics C: Mechanics · Kinematics

  1. 40 m/s and 44 m/s^2
  2. 44 m/s and 40 m/s^2
  3. 24 m/s and 20 m/s^2
  4. 40 m/s and 24 m/s^2
Show the worked answer
  1. Velocity is the first derivative: v(t) = 12t^2 - 4t.
  2. At t = 2: 12(4) - 8 = 48 - 8 = 40 m/s.
  3. Acceleration is the second derivative: a(t) = 24t - 4.
  4. At t = 2: 48 - 4 = 44 m/s^2.

Answer: 40 m/s and 44 m/s^2

Question 2: An Atwood machine has masses of 3 kg and 5 kg on a light frictionless pulley. What is the acceleration? Use g = 9.8 m/s^2.

AP Physics C: Mechanics · Force and Translational Dynamics

  1. 2.45 m/s^2
  2. 9.8 m/s^2
  3. 1.96 m/s^2
  4. 4.9 m/s^2
Show the worked answer
  1. The net driving force is the weight difference: (5 - 3) x 9.8 = 19.6 N.
  2. The whole system that has to accelerate is 5 + 3 = 8 kg.
  3. a = net force / total mass = 19.6 / 8.
  4. That equals 2.45 m/s^2.

Answer: 2.45 m/s^2

Question 3: A variable force F(x) = 3x^2 newtons acts along the x-axis. How much work does it do from x = 0 to x = 2 m?

AP Physics C: Mechanics · Work, Energy, and Power

  1. 8 J
  2. 12 J
  3. 6 J
  4. 4 J
Show the worked answer
  1. For a force that changes with position, work is the integral of F dx.
  2. The antiderivative of 3x^2 is x^3.
  3. At x = 2: 2^3 = 8. At x = 0 it is 0.
  4. So the work done is 8 J.

Answer: 8 J

Question 4: A force F(t) = 6t newtons acts on an object from t = 0 to t = 2 s. What impulse does it deliver?

AP Physics C: Mechanics · Linear Momentum

  1. 12 N s
  2. 24 N s
  3. 6 N s
  4. 3 N s
Show the worked answer
  1. Impulse is the integral of force over time.
  2. The antiderivative of 6t is 3t^2.
  3. At t = 2: 3(4) = 12. At t = 0 it is 0.
  4. The impulse is 12 N s, which also equals the change in momentum.

Answer: 12 N s

Question 5: What is the rotational inertia of a uniform solid disk of mass 4 kg and radius 0.5 m about its center?

AP Physics C: Mechanics · Torque and Rotational Dynamics

  1. 0.5 kg m^2
  2. 1.0 kg m^2
  3. 0.25 kg m^2
  4. 2.0 kg m^2
Show the worked answer
  1. For a solid disk about its central axis, I = one half M R squared.
  2. R squared is 0.5^2 = 0.25.
  3. M times R squared is 4 x 0.25 = 1.0.
  4. Half of 1.0 is 0.5 kg m^2.

Answer: 0.5 kg m^2

Question 6: A skater with rotational inertia 6 kg m^2 spins at 2 rad/s, then pulls in to 3 kg m^2. What is the new angular speed?

AP Physics C: Mechanics · Energy and Momentum of Rotating Systems

  1. 4 rad/s
  2. 1 rad/s
  3. 2 rad/s
  4. 12 rad/s
Show the worked answer
  1. With no external torque, angular momentum I times omega stays constant.
  2. Before: 6 x 2 = 12 kg m^2 per second.
  3. After: 3 x omega = 12.
  4. omega = 4 rad/s. Notice the kinetic energy rises, paid for by the skater's muscles.

Answer: 4 rad/s

Question 7: Simple harmonic motion is described by x = 0.2 cos(5t), in meters and seconds. What are the maximum speed and maximum acceleration?

AP Physics C: Mechanics · Oscillations

  1. 1.0 m/s and 5.0 m/s^2
  2. 0.2 m/s and 1.0 m/s^2
  3. 5.0 m/s and 25 m/s^2
  4. 1.0 m/s and 25 m/s^2
Show the worked answer
  1. Here the amplitude A = 0.2 m and the angular frequency omega = 5 rad/s.
  2. Maximum speed is A times omega: 0.2 x 5 = 1.0 m/s.
  3. Maximum acceleration is A times omega squared: omega squared is 25.
  4. 0.2 x 25 = 5.0 m/s^2.

Answer: 1.0 m/s and 5.0 m/s^2

Question 8: A conservative force has potential energy U(x) = 3x^2 - 12x joules. At what position is the object in equilibrium?

AP Physics C: Mechanics · Work, Energy, and Power

  1. x = 2 m
  2. x = 0 m
  3. x = 4 m
  4. x = 6 m
Show the worked answer
  1. The force is the negative derivative of the potential energy.
  2. dU/dx = 6x - 12, so F = -(6x - 12) = 12 - 6x.
  3. Equilibrium means the force is zero: 12 - 6x = 0.
  4. x = 2 m. The potential has a minimum there, so the equilibrium is stable.

Answer: x = 2 m

Which unit each printed question belongs to

Use this map after marking your work. If two misses share a unit, review that unit before starting a generated set.

The 8 printed AP Physics C: Mechanics questions, the unit each one tests, and its answer.
QuestionUnitWhat it asksAnswer
1KinematicsA particle has position x(t) = 4t^3 - 2t^2 meters. What are its velocity and acceleration at t = 2 s?40 m/s and 44 m/s^2
2Force and Translational DynamicsAn Atwood machine has masses of 3 kg and 5 kg on a light frictionless pulley. What is the acceleration? Use g = 9.8 m/s^2.2.45 m/s^2
3Work, Energy, and PowerA variable force F(x) = 3x^2 newtons acts along the x-axis. How much work does it do from x = 0 to x = 2 m?8 J
4Linear MomentumA force F(t) = 6t newtons acts on an object from t = 0 to t = 2 s. What impulse does it deliver?12 N s
5Torque and Rotational DynamicsWhat is the rotational inertia of a uniform solid disk of mass 4 kg and radius 0.5 m about its center?0.5 kg m^2
6Energy and Momentum of Rotating SystemsA skater with rotational inertia 6 kg m^2 spins at 2 rad/s, then pulls in to 3 kg m^2. What is the new angular speed?4 rad/s
7OscillationsSimple harmonic motion is described by x = 0.2 cos(5t), in meters and seconds. What are the maximum speed and maximum acceleration?1.0 m/s and 5.0 m/s^2
8Work, Energy, and PowerA conservative force has potential energy U(x) = 3x^2 - 12x joules. At what position is the object in equilibrium?x = 2 m

How the generated AP Physics C: Mechanics sets are created

The 8 questions above are fixed and checked. The generator at the top of the page is different: it writes fresh questions with AI from the course and unit information shown here, then the application checks each one for a complete prompt, four choices, one keyed answer, and an explanation. Generated questions are original practice—not official or released exam questions—and AI can still make mathematical mistakes. Verify a disputed answer with the stated method, your course materials, or the MathGPT solver, and follow the site's academic-integrity guidance.

Questions about this AP Physics C: Mechanics course test

What does this page cover?

It covers all 7 AP Physics C: Mechanics units listed above.

When can I see correct answers and explanations?

Submit the full test first. The result screen then shows every response, the correct answer, and the explanation so you can review each miss.

How long is each section of the AP Physics C: Mechanics exam?

Multiple choice: 1 hour 25 minutes, 42 questions. Free response: 1 hour 35 minutes, 4 questions.

Which AP Physics C: Mechanics sections allow a graphing calculator?

Rules change from section to section. Multiple choice: four-function, scientific, or graphing calculator. Free response: four-function, scientific, or graphing calculator. Provided for the whole exam: equations and constants table. Practise each section under its own rule.

Which AP Physics C: Mechanics units does this test cover?

All seven: Kinematics, Force and Translational Dynamics, Work, Energy, and Power, Linear Momentum, Torque and Rotational Dynamics, Energy and Momentum of Rotating Systems, Oscillations. Study first: Differential equations from Newton's laws.

What should I check first when I review a missed AP Physics C: Mechanics question?

Solving a separable differential equation and never applying the initial condition. An unresolved constant is an unfinished answer.

What should I do with a missed question?

Classify the miss as a definition, setup, calculation, interpretation, or timing error. Re-solve it from a blank page, then use the MathGPT tutor for a hint or method check.