7 A disc, of mass 0.15 kg , slides across a smooth horizontal table and collides with a vertical wall which is perpendicular to the path of the disc. The disc is in contact with the wall for 0.02 seconds and then rebounds.
A possible model for the force, \(F\) newtons, exerted on the disc by the wall, whilst in contact, is given by $$F = k t ^ { 2 } ( t - b ) ^ { 2 } \quad \text { for } \quad 0 \leq t \leq 0.020$$ where \(k\) and \(b\) are constants.
The force is initially zero and becomes zero again as the disc loses contact with the wall. 7

1. State the value of \(b\).
   7
2. Find the magnitude of the impulse on the disc, giving your answer in terms of \(k\).
   7
3. The disc is travelling at \(4 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) when it hits the wall.
   The disc rebounds with a speed of \(2 \mathrm {~m} \mathrm {~s} ^ { - 1 }\)
   Find \(k\).
   [0pt] [3 marks]