A particle \(P\) moving in a straight line has displacement \(x \mathrm{~m}\) from a fixed point \(O\) on the line and velocity \(v \mathrm{~m} \mathrm{~s}^{-1}\) at time \(t \mathrm{~s}\). The acceleration of \(P\), in \(\mathrm{ms}^{-2}\), is given by \(6 v \sqrt{v+9}\). When \(t=0, x=2\) and \(v=72\).
(a) Find an expression for \(v\) in terms of \(x\).
(b) Find an expression for \(x\) in terms of \(t\).