Lesson MC5-MC7

MC5-MC7 Variable forces and power Quiz: AQA Further Maths, Unit 3

20 questions

Written by Revision Ninja · Last reviewed 11 October 2026

In partnership with Revision Ninja

Lesson MC5-MC7, Variable forces and power: 20 multiple choice questions for the AQA Further Maths (7367), Unit 3: Optional application 1: mechanics, written with Revision Ninja.

Host it live on the board and students join with a game code on their own devices, or revise alone with Free Play. The answers are revealed in the game.

Host this setFree Play

The 20 questions

  1. Which expression gives the work done by a variable force F(x) on a particle moving from x = a to x = b?

    • F(b) minus F(a)
    • The integral of x F(x) with respect to x from a to b
    • The integral of F(x) with respect to x from a to b
    • The product F(a) times (b minus a)

  2. A spring of stiffness k is extended by a distance x from its natural length. What is its elastic potential energy?

    • kx/2
    • kx^2/4
    • kx^2/2
    • 2kx^2

  3. What is the SI unit of power?

    • The watt
    • The newton per metre
    • The newton second
    • The joule

  4. A force F acts along the direction of motion of a particle moving with speed v. What is the power developed by the force?

    • F divided by v
    • F plus v
    • F multiplied by v squared
    • F multiplied by v

  5. An elastic string has modulus of elasticity lambda and natural length l. When it is extended by x, what is its elastic potential energy?

    • lambda l x^2 divided by 2
    • lambda x^2 divided by l
    • lambda x divided by 2l
    • lambda x^2 divided by 2l

  6. For an elastic spring of stiffness k, which expression gives the tension T when the spring is extended by x?

    • T = k divided by x
    • T = kx^2
    • T = x divided by k
    • T = kx

  7. In a problem with no dissipative forces, which statement about mechanical energy is always true?

    • Work done by the tension is always positive
    • Potential energy always equals kinetic energy
    • Kinetic energy is constant throughout the motion
    • Total kinetic energy plus potential energy is constant

  8. A variable force F = 3x^2 newtons acts along the x-axis. What is the work done as the particle moves from x = 0 m to x = 4 m?

    • 24 J
    • 16 J
    • 64 J
    • 48 J

  9. A variable force F = 6x + 2 newtons acts along the x-axis. What is the work done as the particle moves from x = 0 m to x = 2 m?

    • 14 J
    • 16 J
    • 20 J
    • 12 J

  10. A spring has stiffness 40 N/m. What is its elastic potential energy when extended by 0.2 m?

    • 8 J
    • 0.8 J
    • 1.6 J
    • 0.4 J

  11. An elastic string has modulus 20 N and natural length 0.5 m. What is its elastic potential energy when extended by 0.1 m?

    • 0.1 J
    • 2 J
    • 0.4 J
    • 0.2 J

  12. A car engine delivers a constant driving force of 1200 N at a speed of 15 m/s. What power is being delivered?

    • 1.2 kW
    • 80 W
    • 180 kW
    • 18 kW

  13. A 0.5 kg particle on a smooth horizontal table is pushed from rest by a spring of stiffness 50 N/m compressed by 0.4 m. What is its speed when the spring reaches its natural length?

    • 2 m/s
    • 4 m/s
    • 16 m/s
    • 0.8 m/s

  14. A car of constant power 30 kW moves at a constant speed of 25 m/s on a level road. What is the resistive force opposing its motion?

    • 1500 N
    • 12000 N
    • 1200 N
    • 750 N

  15. A variable force F = 2 + 3x newtons acts along the x-axis. What is the work done as the particle moves from x = 0 to x = 2 metres?

    • 13 J
    • 6 J
    • 10 J
    • 8 J

  16. A variable force F = 6 sqrt(x) newtons acts along the x-axis. What is the work done as the particle moves from x = 0 to x = 4 metres?

    • 16 J
    • 32 J
    • 48 J
    • 24 J

  17. A particle of mass 0.5 kg is on a smooth table attached to a spring of stiffness 80 N/m and natural length 1 m. It is released from rest when extended by 0.3 m. What is its speed at the natural length?

    • 3.6 m/s
    • sqrt(7.2) m/s
    • sqrt(28.8) m/s
    • sqrt(14.4) m/s

  18. A car moves at constant speed v against a resistance proportional to its speed, R = 60v newtons. What power is needed to maintain a speed of 20 m/s?

    • 1.2 kW
    • 12 kW
    • 48 kW
    • 24 kW

  19. An elastic string has modulus 50 N and natural length 1 m. What is the work done in stretching it from an extension of 0.1 m to an extension of 0.3 m?

    • 2 J
    • 8 J
    • 0.5 J
    • 4 J

  20. A variable resistive force F = 4x - x^2 newtons acts on a particle from x = 0 to x = 3 metres. What is the work done against this force?

    • 12 J
    • 18 J
    • 9 J
    • 4.5 J

All AQA Further Maths quizzes