2.43: Kinematics with velocity inversely proportional to a cube

0606/22/M/J/19 — Question 11 · 9 marks

The velocity, v ms1v\text{ ms}^{-1}, of a particle travelling in a straight line, tt seconds after passing through a fixed point OO, is given by v=4(t+1)3v = \dfrac{4}{(t + 1)^{3}}.
(i)
Explain why the direction of motion of the particle never changes.
[1]
(ii)
Showing all your working, find the acceleration of the particle when t=5t = 5.
[3]
(iii)
Find an expression for the displacement of the particle from OO after tt seconds.
[3]
(iv)
Find the distance travelled by the particle in the fourth second.
[2]