A particle moves in a straight line such that its displacement, \(s\) metres, from a fixed point \(O\) at time \(t\) seconds, is given by

\(s=4+\cos3t,\qquad t\geq0.\)

The particle is initially at rest.

(i) Find the exact value of \(t\) when the particle is next at rest.

(ii) Find the distance travelled by the particle between \(t=\dfrac{\pi}{4}\) and \(t=\dfrac{\pi}{2}\) seconds.

(iii) Find the greatest acceleration of the particle.