4C.5.1 Kinematics of a particle moving in a straight line with variable acceleration Quiz: Pearson Edexcel Further Maths, Unit 34

The 20 questions

1. Which expression gives the velocity v of a particle whose displacement is x(t)?

   • dx/dt
   • x/t
   • d^2x/dt^2
   • dv/dt

2. How is displacement found from a known velocity function?

   • Integration
   • Differentiation
   • Substitution
   • Factorisation

3. How is velocity found from a known acceleration function?

   • Squaring
   • Integration
   • Inverting
   • Differentiation

4. What determines the constant of integration in kinematics problems?

   • Total time
   • Final velocity
   • Maximum height
   • Initial conditions

5. In which direction is a particle moving if its velocity is negative?

   • Positive direction
   • At rest
   • Upwards
   • Negative direction

6. What happens to speed when acceleration opposes the direction of velocity?

   • Becomes zero
   • Remains constant
   • Increases
   • Decreases

7. The area under a velocity-time graph gives the

   • acceleration
   • force
   • displacement
   • momentum

8. A particle has velocity v = 3t^2 - 6t and x = 0 at t = 0. What is its displacement at t = 3 s?

   • 0 m
   • 9 m
   • -9 m
   • 27 m

9. A particle has acceleration a = 6t - 4 and velocity 2 m/s at t = 0. What is its velocity at t = 2 s?

   • 6 m/s
   • 2 m/s
   • 10 m/s
   • 4 m/s

10. A particle has acceleration a = 2x and starts from rest at x = 0. What is its speed at x = 3 m?

    • sqrt(6) m/s
    • 3 sqrt(2) m/s
    • 9 m/s
    • 6 m/s

11. A particle has acceleration a = -2v and speed 10 m/s at t = 0. What is its speed at t = 1 s?

    • 5 m/s
    • 8 m/s
    • 10 e^(-2) m/s, about 1.35 m/s
    • 10 e^2 m/s

12. A particle has displacement x = t^3 - 6t^2 + 9t. What is its velocity at t = 1 s?

    • 0 m/s
    • -3 m/s
    • 6 m/s
    • 3 m/s

13. A particle has acceleration a = 12 - 3t^2 and starts from rest at t = 0. What is its velocity at t = 2 s?

    • 12 m/s
    • 16 m/s
    • 24 m/s
    • 8 m/s

14. A particle has velocity v = 4 + 2x m/s. What is its acceleration at x = 3 m?

    • 16 m/s^2
    • 10 m/s^2
    • 14 m/s^2
    • 20 m/s^2

15. A particle has velocity v = 2t + 3 m/s and x = 1 m at t = 0. What is its displacement at t = 2 s?

    • 9 m
    • 13 m
    • 7 m
    • 11 m

16. A particle starts from rest at the origin with acceleration a = 4 - 2t m/s^2. What is its displacement when it next comes to rest?

    • 64/3 m
    • 16 m
    • 8/3 m
    • 32/3 m

17. A particle has velocity v = 3 sqrt(x) m/s. What is its acceleration at x = 4 m?

    • 9 m/s^2
    • 4.5 m/s^2
    • 1.5 m/s^2
    • 6 m/s^2

18. A particle starts from rest and has acceleration a = 10 - 0.5v m/s^2. What is its limiting speed?

    • 20 m/s
    • 5 m/s
    • 10 m/s
    • 40 m/s

19. What feature of integration requires using an initial condition for displacement?

    • Gradient function
    • Additive constant
    • Derivative factor
    • Upper limit

20. A particle starts from rest with acceleration a = 12 - 2t m/s^2. At what time is its velocity greatest?

    • 12 s
    • 6 s
    • 3 s
    • 2 s

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