Calculus kinematics quiz for AP Physics C: 10 questions with answers

by aicko
28 October 202628 October 2026

Quick answer: In calculus-based kinematics, velocity is the derivative of position and acceleration is the derivative of velocity. This AP Physics C quiz checks calculus kinematics with 10 multiple-choice questions and instant feedback; every answer comes with a short explanation.

Calculus kinematics quiz for AP Physics C: 10 questions with answers

This calculus kinematics quiz for AP Physics C has quick multiple-choice questions with instant feedback. Need a refresher first? Read the lesson or do the worksheet on calculus kinematics.

Choose the best answer for each question. Typical traps are forgetting the constants of integration, using constant-acceleration equations and confusing displacement with distance.

Level: AP Physics C (Mechanics and E&M, calculus-based) · Curriculum: AP PC:M Unit 1

Contents

Calculus kinematics quiz: the questions

Which expression gives the velocity from a position function x(t)?

x = 3t² − 2t. What is the acceleration?

A student shades the region under a velocity–time curve. What does its area give?

A particle has a = 6t and v(0) = 2 m/s. What is v at t = 2 s?

When is speed decreasing?

Which relation gives v as a function of x when a depends on x?

For x = t³ − 6t² + 9t, at what times is the particle at rest?

The distance travelled is greater than the displacement when the particle...

What is the maximum speed of x = A sin(ωt)?

What is wrong with using v = v₀ + at when a = 4t?

Velocity from position? — v = dx/dt

Acceleration from velocity? — a = dv/dt = d²x/dt²

Slope of an x–t graph? — Velocity

Area under a v–t graph? — Displacement

Area under an a–t graph? — Change in velocity

Position from velocity? — x = x₀ + ∫v dt

Acceleration in terms of x? — a = v dv/dx

Speed increases when? — v and a have the same sign

Distance versus displacement? — Distance integrates |v|

What do integration constants fix? — Initial conditions v₀ and x₀

Follow us