(i)[2]
Determine the steady speed of the car on a horizontal road, assuming that the engine operates at $20\,\text{kW}$.
(ii)[3]
On a hill inclined at angle $\theta$ to the horizontal, where $\sin \theta = \frac{1}{7}$, the car is travelling at constant speed of $10\,\text{m s}^{-1}$. Find the power of the car’s engine.
(iii)[3]
The car goes down the same hill, and the engine is working at $80\%$ of the power found in part (ii). Determine the car’s acceleration at the instant when the speed is $20\,\text{m s}^{-1}$.