4 A particle of mass 0.5 kg is initially at rest. The particle then moves in a straight line under the action of a single force. This force acts in a constant direction and has magnitude \(\left( t ^ { 3 } + t \right) \mathrm { N }\), where \(t\) is the time, in seconds, for which the force has been acting.

1. Find the magnitude of the impulse exerted by the force on the particle between the times \(t = 0\) and \(t = 4\).
2. Hence find the speed of the particle when \(t = 4\).
3. Find the time taken for the particle to reach a speed of \(12 \mathrm {~ms} ^ { - 1 }\).