(a(i))[2]
On a horizontal stretch of road, the car is moving at a steady speed of $32\,\text{m s}^{-1}$ and a constant resistive force of $750\,\text{N}$ opposes the motion. Calculate, in kW, the power developed by the car’s engine.
(a(ii))[3]
If this power is suddenly reduced by $8\,\text{kW}$, determine the car’s instantaneous deceleration.
(b)[5]
On a part of the road inclined at $\sin^{-1} 0.096$ to the horizontal, the resistive force on the car is $(1000 + 8v)\,\text{N}$ when its speed is $v\,\text{m s}^{-1}$. The car moves up this slope at constant speed while the engine operates at $60\,\text{kW}$. Find the constant speed.