A particle \(P\) moves in a straight line, such that its displacement, \(x\) m, from a fixed point \(O\), \(t\) s after passing \(O\), is given by

\(x=4\cos(3t)-4.\)

(i) Find the velocity of \(P\) at time \(t\).

(ii) Hence write down the maximum speed of \(P\).

(iii) Find the smallest value of \(t\) for which the acceleration of \(P\) is zero.

(iv) For the value of \(t\) found in part (iii), find the distance of \(P\) from \(O\).