2.8: Displacement, distance travelled and greatest acceleration

0606/21/M/J/18 — Question 10 · 7 marks

A particle moves in a straight line such that its displacement, ss metres, from a fixed point OO at time tt seconds, is given by s=4+cos3ts = 4 + \cos 3t, where t0t \ge 0. The particle is initially at rest.
(i)
Find the exact value of tt when the particle is next at rest.
[2]
(ii)
Find the distance travelled by the particle between t=π4t = \tfrac{\pi}{4} and t=π2t = \tfrac{\pi}{2} seconds.
[3]
(iii)
Find the greatest acceleration of the particle.
[2]