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

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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.

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The 20 questions

  1. What mathematical operation on force F(x) with respect to x gives work done?

    • Differentiation
    • Factorisation
    • Integration
    • Multiplication

  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. Which SI unit is used to measure power?

    • Pascal
    • Watt
    • Newton
    • 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 system with no dissipative forces, what mechanical quantity remains constant?

    • Linear momentum
    • Total energy
    • Kinetic energy
    • Potential energy

  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

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