Mathematics 9709 · AS & A Level · Energy, work and power
Energy, work and power — practice question
A car with mass $900\,\text{kg}$ is travelling uphill on a slope of angle $\sin^{-1}(0.12)$ above the horizontal. Its starting speed is $11\,\text{m s}^{-1}$. After $12\,\text{s}$, it has covered $150\,\text{m}$ up the slope and is moving at $16\,\text{m s}^{-1}$. The car’s engine is outputting power at a steady rate of $24\,\text{kW}$.
(a)[5]
Determine the work done against the resistive forces over the $12\,\text{s}$.
(b)[3]
The car then moves along a straight horizontal road. The resistive force acting on it is $(1520 + 4v)\,\text{N}$ when its speed is $v\,\text{m s}^{-1}$. It travels at constant speed while the engine operates at a constant rate of $32\,\text{kW}$. Determine this speed.
Worked solution & mark scheme
This 8-mark question has a full step-by-step worked solution and mark scheme. One marking point: “A correct calculation of the change in kinetic energy.” …