A particle moves in a straight line, such that its velocity, \(v\text{ ms}^{-1}\), \(t\) s after passing a fixed point \(O\), is given by

\(v=2+6t+3\sin2t.\)

(i) Find the acceleration of the particle at time \(t\).

(ii) Hence find the smallest value of \(t\) for which the acceleration of the particle is zero.

(iii) Find the displacement, \(x\) m from \(O\), of the particle at time \(t\).