3 A particle \(A\) of mass 0.5 kg is moving with a speed of \(3.15 \mathrm {~ms} ^ { - 1 }\) on a smooth horizontal surface when it collides directly with a particle \(B\) of mass 0.8 kg which is at rest on the surface. The velocities of \(A\) and \(B\) immediately after the collision are denoted by \(\mathrm { v } _ { \mathrm { A } } \mathrm { ms } ^ { - 1 }\) and \(\mathrm { v } _ { \mathrm { B } } \mathrm { ms } ^ { - 1 }\) respectively. You are given that \(\mathrm { v } _ { \mathrm { B } } = 2 \mathrm { v } _ { \mathrm { A } }\).

1. Find the values of \(\mathrm { V } _ { \mathrm { A } }\) and \(\mathrm { V } _ { \mathrm { B } }\).
2. Find the coefficient of restitution between \(A\) and \(B\).
3. Explain why the coefficient of restitution is a dimensionless quantity.
4. Calculate the total loss of kinetic energy as a result of the collision.
5. State, giving a reason, whether or not the collision is perfectly elastic.
6. Calculate the impulse that \(B\) exerts on \(A\) in the collision.