A toy rocket, of mass 1 kg, is modelled as a particle. It is launched from rest using its engines, which produce a force of size (20 - t) and have enough fuel for five seconds. After five seconds the rocket will be subject to one force only: its weight.

a. Show that, for 0 ≤ t ≤ 5, dv/dt = 2(5 – t).

b. Find the velocity when t = 5s.

c. Find the maximum height achieved, to the nearest metre.