3. A particle \(P\) of mass 2 kg is moving with speed \(u \mathrm {~m} \mathrm {~s} ^ { - 1 }\) in a straight line on a smooth horizontal plane. The particle \(P\) collides directly with a particle \(Q\) of mass 4 kg which is at rest on the same horizontal plane. Immediately after the collision, \(P\) and \(Q\) are moving in opposite directions and the speed of \(P\) is one-third the speed of \(Q\).

1. Show that the speed of \(P\) immediately after the collision is \(\frac { 1 } { 5 } u \mathrm {~m} \mathrm {~s} ^ { - 1 }\). After the collision \(P\) continues to move in the same straight line and is brought to rest by a constant resistive force of magnitude 10 N . The distance between the point of collision and the point where \(P\) comes to rest is 1.6 m .
2. Calculate the value of \(u\).
   (5)