A particle \(P\) moves in a straight line. The displacement of \(P\) from a fixed point \(O\) is \(x\) metres at time \(t\) seconds. The particle passes through \(O\) when \(t=0\), and its velocity \(v\) metres per second is given by

\(v=12e^{2t}-48t,\qquad t\geq0.\)

(i) Find \(x\) in terms of \(t\).

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

(iii) Find the velocity of \(P\) when its acceleration is zero.