A particle \(P\) moves in a straight line. Its acceleration, \(a\,\mathrm{m\,s^{-2}}\), is given by

\(a=6t\quad\text{for }0\leq t\leq3,\)

and

\(a=\frac{18\mathrm e^3}{\mathrm e^t}\quad\text{for }t\geq3.\)

When \(t=1\), the velocity of \(P\) is \(2\,\mathrm{m\,s^{-1}}\) and the displacement of \(P\) from \(O\) is \(-4\) metres.

(a)(i) Find the velocity of \(P\) when \(t=3\).

(a)(ii) Find the displacement of \(P\) from \(O\) when \(t=3\).

(b) Find an expression, in terms of \(t\), for the displacement of \(P\) from \(O\) when \(t\geq3\).