Lesson 4C.4.1

4C.4.1 Newton's laws of motion for particles Quiz: Pearson Edexcel Further Maths, Unit 33

20 questions

Written by Revision Ninja · Last reviewed 11 October 2026

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Lesson 4C.4.1, Newton's laws of motion for particles: 20 multiple choice questions for the Pearson Edexcel Further Maths (9FM0), Unit 33: Newton's laws and simple harmonic motion, written with Revision Ninja.

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The 20 questions

  1. For a particle moving in one dimension under a variable force F(x), which equation is correct?

    • m dx/dt = F(x)
    • m v dv/dx = F(x)
    • F(x) = m v^2
    • m dv/dx = F(x)

  2. What is the magnitude of the gravitational force between masses M and m a distance r apart?

    • Gm/r^2
    • GMm r^2
    • GMm/r^2
    • GMm/r

  3. Which equation gives v^2 after integrating a = v dv/dx with respect to x?

    • x = integral of v dv
    • v = integral of a dx
    • v^2 = 2 integral of a dx + constant
    • v^2 = integral of a dt

  4. What is the purpose of the constant of integration when finding velocity from acceleration?

    • it is fixed by the initial conditions
    • it equals the mass of the particle
    • it equals the acceleration
    • it equals the total distance travelled

  5. Newton's first law states that a particle remains at rest or moves uniformly unless

    • gravity acts on it
    • acted on by a resultant force
    • it has a non-zero mass
    • its acceleration is constant

  6. Newton's third law says that action and reaction forces are

    • unequal in magnitude
    • equal and in the same direction
    • equal and acting on the same body
    • equal and opposite, acting on different bodies

  7. What is the SI unit of force?

    • newton (kg m s^-2)
    • newton per second
    • joule (kg m^2 s^-2)
    • kg m s^-1

  8. A particle of mass 1 kg starts from rest at x = 0 and moves under a resultant force F = 3x newtons. What is its speed at x = 2 m?

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

  9. A particle is at distance 2R from the centre of a planet of radius R. Compared with its weight at the surface, its weight at this point is

    • one eighth
    • twice
    • one half
    • one quarter

  10. A particle is released from rest at x = a and is attracted towards O with acceleration mu/x^2. What is its speed when x = a/2?

    • sqrt(2mu/a)
    • sqrt(mu/a)
    • sqrt(4mu/a)
    • sqrt(mu/(2a))

  11. A particle of mass 2 kg has resultant force F = 4t newtons and starts from rest. What is its velocity at t = 3 s?

    • 6 m/s
    • 18 m/s
    • 9 m/s
    • 4.5 m/s

  12. What distance from the centre of the Earth gives a weight equal to one ninth of the surface weight?

    • 9R
    • 4.5R
    • R/3
    • 3R

  13. A particle of unit mass moves with resultant force -kv opposing its motion, starting with speed u. What is its speed at time t?

    • u e^(kt)
    • u(1 - kt)
    • u - kt
    • u e^(-kt)

  14. A particle of mass 2 kg has resultant force F = 10 - 2x newtons along the x-axis. What is its acceleration at x = 2 m?

    • 5 m/s^2
    • 3 m/s^2
    • 1.5 m/s^2
    • 8 m/s^2

  15. A particle of mass 1 kg starts at rest with resultant force F = 2t newtons. What is the impulse from t = 0 to t = 3 s?

    • 18 N s
    • 6 N s
    • 9 N s
    • 3 N s

  16. A particle is projected vertically upwards from the surface of a planet of radius R with surface gravity g. What speed is needed to escape to infinity?

    • sqrt(2gR)
    • sqrt(gR/2)
    • sqrt(2g/R)
    • sqrt(gR)

  17. A particle of mass m moves in a straight line with resistance mkv^2, starting with speed u. Does it stop in a finite distance?

    • Yes, after distance ln(2)/k
    • Yes, after distance u/k
    • No, v = u e^(-kx), so the speed never reaches zero
    • Yes, after distance 1/(ku)

  18. A particle released from rest at distance 4a from the centre of an inverse square attraction with constant mu = GM reaches distance a. What is its speed there?

    • sqrt(3mu/a)
    • sqrt(2mu/a)
    • sqrt(3mu/(2a))
    • sqrt(mu/(2a))

  19. Why is a = v dv/dx preferred to a = dv/dt when the force depends on position?

    • Velocity is always constant with position
    • Displacement is always constant
    • dv/dt is always zero when the force depends on position
    • It links velocity directly to displacement, so an equation in x can be integrated without needing time

  20. A particle of mass 2 kg has resultant force 6 - 3v newtons, where v is its speed in m/s, and starts from rest. What is its terminal speed?

    • 4 m/s
    • 3 m/s
    • 2 m/s
    • 6 m/s

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