Lesson Q4

Q4 Calculus in kinematics Quiz: AQA Maths, Unit 12

20 questions

Written by Revision Ninja · Last reviewed 11 October 2026

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Lesson Q4, Calculus in kinematics: 20 multiple choice questions for the AQA Maths (7357), Unit 12: Mechanics, written with Revision Ninja.

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The 20 questions

  1. Which expression gives velocity from displacement r(t)?

    • the integral of r with respect to t
    • d^2r/dt^2
    • r/t
    • dr/dt

  2. Which expression gives acceleration from velocity v(t)?

    • dr/dt
    • v/t
    • the integral of v with respect to t
    • dv/dt

  3. Which expression gives displacement from velocity?

    • r = integral of a dt
    • r = d(v)/dt for every t
    • r = integral of v dt
    • r = dv/dt

  4. When finding v = integral of a dt, what extra term must be included?

    • A constant of integration fixed by the initial velocity
    • No constant, since integration removes constants
    • A constant of integration that is always zero
    • The initial displacement

  5. A particle has r = 3t^2 - 2t in metres. What is its velocity at t = 2 s?

    • 14 m s^-1
    • 8 m s^-1
    • 10 m s^-1
    • 12 m s^-1

  6. For r = 3t^2 - 2t, what is the acceleration at any time t?

    • 6t m s^-2
    • 6 m s^-2
    • 6t - 2 m s^-2
    • 3 m s^-2

  7. A particle has v = 4t^3 - 6t. What is its acceleration at t = 1 s?

    • -2 m s^-2
    • 6 m s^-2
    • 18 m s^-2
    • 12 m s^-2

  8. A particle has v = 2t + 3 and starts at the origin. What is its displacement at t = 4 s?

    • 28 m
    • 14 m
    • 20 m
    • 40 m

  9. A particle starts from rest with a = 4 - 2t. At what time is its velocity greatest?

    • t = 4 s
    • t = 1 s
    • t = 0 s
    • t = 2 s

  10. A particle starts from rest with a = 4 - 2t. What is its maximum velocity?

    • 2 m s^-1
    • 4 m s^-1
    • 0 m s^-1
    • 8 m s^-1

  11. A particle has v = 6 - 2t from t = 0. What is its displacement when v = 0?

    • 6 m
    • 3 m
    • 18 m
    • 9 m

  12. A particle starts at the origin with u = 10 m s^-1 and a = -2 m s^-2. What total distance does it travel before stopping?

    • 25 m
    • 50 m
    • 10 m
    • 5 m

  13. Why is a = d^2r/dt^2 equivalent to a = dv/dt?

    • Because velocity and displacement have the same units
    • Because r and v always have the same value
    • Because t is constant in every motion
    • Because v = dr/dt, so a = dv/dt = d(dr/dt)/dt = d^2r/dt^2

  14. If r = 5 sin t, what is v?

    • -5 cos t
    • cos t / 5
    • 5 cos t
    • 5 sin t

  15. A particle has v = 3t^2 - 12t + 9 m s^-1. At which times is it at rest?

    • t = 1 and t = 2
    • t = 0 and t = 4
    • t = 2 only
    • t = 1 and t = 3

  16. A particle has v = 3t^2 - 12t + 9 m s^-1. What is its acceleration at t = 1 s?

    • -3 m s^-2
    • -6 m s^-2
    • 6 m s^-2
    • 0 m s^-2

  17. A particle has v = 3t^2 - 12t + 9 m s^-1 and starts at the origin. What is its displacement from t = 0 to t = 3 s?

    • 0 m
    • -4 m
    • 8 m
    • 4 m

  18. For the particle with v = 3t^2 - 12t + 9 m s^-1, what is the total distance from t = 0 to t = 3 s?

    • 0 m
    • 12 m
    • 4 m
    • 8 m

  19. A particle has a = 2t - 4 m s^-2 and u = 6 m s^-1 at t = 0. What is its velocity at t = 3 s?

    • -3 m s^-1
    • 6 m s^-1
    • 3 m s^-1
    • 9 m s^-1

  20. A particle has r = t^3/3 - 2t^2 + 3t. At what time is its acceleration zero?

    • t = 4/3
    • t = 1
    • t = 2
    • t = 3

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