Lesson 3.02f

3.02f Differentiation and integration with respect to time Quiz: OCR Maths, Unit 17

20 questions

Written by Revision Ninja · Last reviewed 11 October 2026

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Lesson 3.02f, Differentiation and integration with respect to time: 20 multiple choice questions for the OCR Maths (H240), Unit 17: Kinematics, written with Revision Ninja.

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The 20 questions

  1. What mathematical operation converts a displacement-time function into a velocity-time function?

    • Substitution
    • Differentiation
    • Integration
    • Factorisation

  2. How is acceleration expressed in terms of velocity v and time t?

    • d^2v/dt^2
    • integral of v dt
    • v/t
    • dv/dt

  3. Which process is used to determine displacement from a given velocity-time function?

    • Differentiation
    • Integration
    • Extrapolation
    • Rationalisation

  4. What kinematic quantity is represented by the second derivative of displacement with respect to time?

    • Velocity
    • Acceleration
    • Speed
    • Jerk

  5. A particle has displacement x = 3t^2 + 2t. What is its velocity at t = 2?

    • 12
    • 8
    • 14
    • 16

  6. A particle has velocity v = 6t - 4. What is its acceleration at t = 3?

    • 6
    • 2
    • 18
    • 14

  7. Velocity is given by v = 3t^2. What is displacement s from t = 0 to t = 2?

    • 8
    • 24
    • 12
    • 6

  8. A particle has velocity v = 4t^3 - 2t. What is its acceleration function a(t)?

    • 4t^2 - 2
    • t^4 - t^2
    • 12t^2
    • 12t^2 - 2

  9. Position is given by r = (t^2)i + (3t)j. What is the velocity vector v?

    • 6ti + 3j
    • 2ti + 3j
    • 2ti + 3tj
    • ti + 3j

  10. Velocity is v = 3i + 4tj. What is the acceleration vector a?

    • 4i
    • 4j
    • 3j
    • 3i + 4j

  11. Position is r = (4t^3)i + (2t)j. What is the acceleration vector at t = 1?

    • 12i
    • 24i + 2j
    • 12i + 2j
    • 24i

  12. What constant must always be added when finding velocity by integrating non-uniform acceleration?

    • Unit vector
    • Initial time
    • Gravity constant
    • Constant of integration

  13. Velocity is v = 6t - 3t^2. At what non-zero time t is acceleration equal to zero?

    • t = 1
    • t = 2
    • t = 3
    • t = 0.5

  14. Position is r = (2t^3 - 6t)i. At what positive time t is the particle instantaneously at rest?

    • t = 3
    • t = 2
    • t = 1
    • t = 6

  15. Acceleration is a = 6t. If velocity v = 4 when t = 0, find v when t = 2.

    • 12
    • 28
    • 8
    • 16

  16. Velocity vector is v = 2i + 3j. What is the magnitude of the velocity vector?

    • sqrt(5)
    • sqrt(13)
    • 13
    • 5

  17. In 2D kinematics, how is the velocity vector v derived from position vector r?

    • r/t
    • dr/dt
    • integral of r dt
    • d^2r/dt^2

  18. Particle displacement is s = t^3 - 6t^2. At what time t > 0 is acceleration zero?

    • t = 4
    • t = 2
    • t = 6
    • t = 3

  19. Under vertical gravity, what is the vertical component of the constant acceleration vector?

    • 0
    • -g/2
    • -g
    • g

  20. Acceleration is a = 12t^2. If particle velocity is 0 at t = 0, find velocity at t = 1.

    • 24
    • 12
    • 3
    • 4

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