4 A particle \(P\) of mass 0.25 kg moves in a straight line on a smooth horizontal surface. At time \(t \mathrm {~s}\) the velocity of \(P\) is \(v \mathrm {~m} \mathrm {~s} ^ { - 1 }\). A variable force of magnitude \(3 t \mathrm {~N}\) opposes the motion of \(P\).

1. Given that \(P\) comes to rest when \(t = 3\), find \(v\) when \(t = 0\).
2. Calculate the distance travelled by \(P\) in the interval \(0 \leqslant t \leqslant 3\).