Take \(g=10\,\mathrm{m\,s^{-2}}\).

A particle starts from rest at \(O\) and moves in a straight line, with acceleration \(a=4\sqrt t\,\mathrm{m\,s^{-2}}\) at time \(t\) seconds after leaving \(O\).

(a) Find its speed at \(t=9\). [2]

(b) Find the time after leaving O when speed in metres per second and distance in metres are numerically equal. [3]