5 A particle \(P\) of mass 0.4 kg moves in a straight line on a horizontal surface and has velocity \(v \mathrm {~m} \mathrm {~s} ^ { - 1 }\) at time \(t \mathrm {~s}\). A horizontal force of magnitude \(k \sqrt { } v \mathrm {~N}\) opposes the motion of \(P\). When \(t = 0 , v = 9\) and when \(t = 2 , v = 4\).

1. Express \(\frac { \mathrm { d } v } { \mathrm {~d} t }\) in terms of \(k\) and \(v\), and hence show that \(v = \frac { 1 } { 4 } ( t - 6 ) ^ { 2 }\).
2. Find the distance travelled by \(P\) in the first 3 seconds of its motion.