2.5: Kinematics: rest positions and acceleration

0606/21/M/J/17 — Question 12 · 9 marks

A particle moves in a straight line so that, tt seconds after passing a fixed point OO, its displacement, ss m, from OO is given by s=1+3tcos5ts = 1 + 3t - \cos 5t.
(i)
Find the distance between the particle's first two positions of instantaneous rest.
[7]
(ii)
Find the acceleration when t=πt = \pi.
[2]