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

\(s=\frac{(2t+1)^{3/2}}{t+1}-1.\)

(a) Show that the velocity of \(P\) at time \(t\) can be written in the form

\(\frac{(2t+1)^{1/2}}{(t+1)^2}(a+bt),\)

where \(a\) and \(b\) are integers to be found.

(b) Show that \(P\) is never at instantaneous rest after passing through \(O\).