3 A particle \(P\) of mass 0.2 kg is projected horizontally with speed \(u \mathrm {~ms} ^ { - 1 }\) from a fixed point \(O\) on a smooth horizontal surface. \(P\) moves in a straight line and, at time \(t \mathrm {~s}\) after projection, \(P\) has speed \(v \mathrm {~m} \mathrm {~s} ^ { - 1 }\) and is \(x \mathrm {~m}\) from \(O\). The only force acting on \(P\) has magnitude \(0.4 v ^ { 2 } \mathrm {~N}\) and is directed towards \(O\).

1. Show that \(\frac { 1 } { v } \frac { \mathrm {~d} v } { \mathrm {~d} x } = - 2\).
2. Hence show that \(v = u \mathrm { e } ^ { - 2 x }\).
3. Find \(u\), given that \(x = 2\) when \(t = 4\).