3 Two small spheres \(P\) and \(Q\) have masses 0.1 kg and 0.2 kg respectively. The spheres are moving directly towards each other on a horizontal plane and collide. Immediately before the collision \(P\) has speed \(4 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) and \(Q\) has speed \(3 \mathrm {~m} \mathrm {~s} ^ { - 1 }\). Immediately after the collision the spheres move away from each other, \(P\) with speed \(u \mathrm {~m} \mathrm {~s} ^ { - 1 }\) and \(Q\) with speed \(( 3.5 - u ) \mathrm { m } \mathrm { s } ^ { - 1 }\).

1. Find the value of \(u\). After the collision the spheres both move with deceleration of magnitude \(5 \mathrm {~m} \mathrm {~s} ^ { - 2 }\) until they come to rest on the plane.
2. Find the distance \(P Q\) when both \(P\) and \(Q\) are at rest.