A particle moves in a straight line starting from rest from a point O. The acceleration of the particle at time t seconds after leaving O is a m/s², where a = 4t^{\frac{1}{2}}.

\((a) Find the speed of the particle when t = 9.\)

(b) Find the time after leaving O at which the speed (in metres per second) and the distance travelled (in metres) are numerically equal.