Lesson 3.02f

3.02f Non-uniform acceleration Quiz: OCR Maths, Unit 17

20 questions

Written by Revision Ninja · Last reviewed 11 October 2026

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Lesson 3.02f, Non-uniform acceleration: 20 multiple choice questions for the OCR Maths (H240), Unit 17: Kinematics, written with Revision Ninja.

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The 20 questions

  1. For a particle moving in a straight line with displacement s at time t, which expression gives the velocity v?

    • v = ds/dt
    • v = s/t
    • v = integral of s dt
    • v = d^2s/dt^2

  2. Which expression gives the acceleration a in terms of displacement s?

    • a = ds/dt
    • a = d^2s/dt^2
    • a = s/t^2
    • a = integral of s dt

  3. If the velocity v is known, which integral gives the displacement s?

    • s = integral of v^2 dt
    • s = integral of v dt
    • s = v/t
    • s = integral of a dt

  4. How is velocity obtained from a function for non-uniform acceleration a(t)?

    • Multiply by displacement
    • Differentiate acceleration
    • Integrate acceleration
    • Divide by time

  5. What is evaluated using an initial condition when integrating acceleration to find velocity?

    • Constant of integration
    • Total displacement
    • Gradient
    • Maximum velocity

  6. If a particle has zero velocity at an instant, what is true about its acceleration?

    • Can be non-zero
    • Is always infinite
    • Is always negative
    • Must be zero

  7. In two dimensions the position vector is r = x i + y j. Which expression gives the velocity vector?

    • v = dr/dt = (dx/dt) i + (dy/dt) j
    • v = integral of r dt
    • v = (x + y) i + (x - y) j
    • v = r/t

  8. A particle has displacement s = t^3 - 6t^2 + 9t metres at time t seconds. What is its velocity at t = 2 s?

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

  9. A particle has displacement s = t^3 - 6t^2 + 9t metres at time t seconds. What is its acceleration at t = 2 s?

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

  10. A particle starts from rest at the origin with acceleration a = 4t m s^-2. What is its displacement at t = 3 s?

    • 18 m
    • 12 m
    • 24 m
    • 36 m

  11. A particle has velocity v = 3t^2 m s^-1 and displacement s = 2 m when t = 0. What is its displacement at t = 2 s?

    • 14 m
    • 6 m
    • 10 m
    • 8 m

  12. A particle has velocity v = t^2 - 5t + 4 m s^-1 for t >= 0. At which times is the particle momentarily at rest?

    • t = 2 s and t = 3 s
    • t = 0 s only
    • t = 1 s and t = 4 s
    • t = 4 s and t = 5 s

  13. A particle has velocity v = 4t - t^2 m s^-1. At what time is its acceleration zero?

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

  14. A particle has position vector r = (t^2 i + 3t j) m. What is its velocity at t = 2 s?

    • 4i + 3j m s^-1
    • 2i + 6j m s^-1
    • 4i + 6j m s^-1
    • 2i + 3j m s^-1

  15. A particle has acceleration a = (6t i - 2j) m s^-2 and starts from rest. What is its velocity at t = 1 s?

    • (3i - 4j) m s^-1
    • (6i - 2j) m s^-1
    • (6i - 4j) m s^-1
    • (3i - 2j) m s^-1

  16. A particle has velocity 3i - 2j m s^-1 at t = 1 s. What is its speed at this instant, to 2 decimal places?

    • 1 m s^-1
    • 3.61 m s^-1
    • 13 m s^-1
    • 5 m s^-1

  17. A particle has displacement s = t^3 - 3t^2 metres for t >= 0. What is the total distance travelled from t = 0 to t = 3 s?

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

  18. A particle has acceleration a = 6t - 4 m s^-2 and velocity v = 2 m s^-1 at t = 0. What is its velocity at t = 2 s?

    • 2 m s^-1
    • 6 m s^-1
    • 10 m s^-1
    • 14 m s^-1

  19. A particle has velocity v = 4t - t^2 m s^-1 for 0 <= t <= 5 with s = 0 at t = 0. What is the total distance travelled from t = 0 to t = 5 s?

    • 13 m
    • 10 m
    • 8.33 m
    • 8 m

  20. At a particle's turning point, what is its instantaneous velocity?

    • Zero
    • Equal to acceleration
    • Maximum
    • Negative constant

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