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

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. What expression equals v squared when integrating a = v dv/dx?

   • square root of a dx
   • half integral of a dx
   • integral of a dx
   • 2 integral of a dx

4. When finding velocity by integrating an acceleration equation, how is the integration constant determined?

   • maximum displacement
   • gravitational field
   • final velocity
   • initial conditions

5. According to Newton's first law, when does a particle change its state of uniform motion?

   • zero acceleration
   • constant speed
   • resultant force acting
   • balanced forces

6. How do action and reaction forces relate under Newton's third law?

   • different and opposite
   • equal and same direction
   • equal and opposite
   • proportional and perpendicular

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. Does a particle slowed by resistance mkv squared stop in a finite distance?

    • Yes
    • Depends on initial speed
    • Depends on mass
    • No

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. Which variables are linked when using the acceleration form a = v dv/dx?

    • force and time
    • velocity and displacement
    • displacement and time
    • velocity and 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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