1. A particle \(A\) of mass \(3 m\) and a particle \(B\) of mass \(m\) are moving along the same straight line on a smooth horizontal surface. The particles are moving in opposite directions towards each other when they collide directly.

Immediately before the collision, the speed of \(A\) is \(k u\) and the speed of \(B\) is \(u\). Immediately after the collision, the speed of \(A\) is \(v\) and the speed of \(B\) is \(2 v\). The magnitude of the impulse received by \(B\) in the collision is \(\frac { 3 } { 2 } m u\).

1. Find \(v\) in terms of \(u\) only.
2. Find the two possible values of \(k\).