A particle moving in a straight line passes through a fixed point \(O\). Its velocity, \(v\text{ m s}^{-1}\), \(t\) seconds after passing through \(O\), is given by

\(v=3\cos 2t-1\), for \(t\ge0\).

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

(ii) Find the displacement from \(O\) when \(t=\dfrac{\pi}{4}\).

(iii) Find the acceleration of the particle when it is first at rest.