(a(i))[2]
Calculate the work done against the resisting force in the first $8\,\text{s}$ as the car travels along a horizontal stretch of road at a steady speed of $36\,\text{m s}^{-1}$.
(a(ii))[2]
Calculate the engine power developed by the car, in kW.
(a(iii))[3]
If this power is then increased suddenly by $12\,\text{kW}$, find the instantaneous acceleration of the car.
(b)[2]
The car now moves at a steady speed of $32\,\text{m s}^{-1}$ up a road section inclined at $\theta^\circ$ to the horizontal, with the engine operating at $64\,\text{kW}$. Find the value of $\theta$.
(iii)[3]
If this power is then increased suddenly by $12\text{ kW}$, find the instantaneous acceleration of the car.