Mathematics 9709 · AS & A Level · Energy, work and power
Energy, work and power — practice question
A high-speed train, with a mass of $490\,000\,\text{kg}$, travels along a straight horizontal track at a steady speed of $85\,\text{m s}^{-1}$. Its engines provide $4080\,\text{kW}$ of power.
((i))[1]
Show that the resistance force is $48\,000\,\text{N}$.
((ii))[3]
The train then reaches a hill that is inclined at an angle $\theta^\circ$ to the horizontal, where $\sin \theta^\circ = \frac{1}{200}$. Assuming the resistance force stays the same, determine the power needed for the train to continue at the same constant speed of $85\,\text{m s}^{-1}$.
Worked solution & mark scheme
This 4-mark question has a full step-by-step worked solution and mark scheme.