3 A particle \(P\) of mass 0.25 kg is projected horizontally with speed \(5 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) from a fixed point \(O\) on a smooth horizontal surface and moves in a straight line on the surface. The only horizontal force acting on \(P\) has magnitude \(0.2 v ^ { 2 } \mathrm {~N}\), where \(v \mathrm {~m} \mathrm {~s} ^ { - 1 }\) is the velocity of \(P\) at time \(t \mathrm {~s}\) after it is projected from \(O\). This force is directed towards \(O\).

1. Find an expression for \(v\) in terms of \(t\). The particle \(P\) passes through a point \(X\) with speed \(0.2 \mathrm {~m} \mathrm {~s} ^ { - 1 }\).
2. Find the average speed of \(P\) for its motion between \(O\) and \(X\).