Mathematics 9709 · AS & A Level · Energy, work and power

Energy, work and power — practice question

A straight hill $AB$ is $400\,\text{m}$ long, with $A$ at the summit and $B$ at the foot, and it makes an angle of $4^\circ$ to the horizontal. A straight level road $BC$ is $750\,\text{m}$ long. A car of mass $1250\,\text{kg}$ has speed $5\,\text{m s}^{-1}$ at $A$ as it begins to travel downhill. During the descent, the resistive force on the car is $2000\,\text{N}$ and the driving force remains constant. The car’s speed on arriving at $B$ is $8\,\text{m s}^{-1}$. At $B$ the car continues along road $BC$. The driving force stays constant and is twice its value on the hill. The resistive force on the car remains $2000\,\text{N$}.
(i)[5]

Using work and energy, calculate the driving force of the car.

(ii)[3]

Calculate the acceleration of the car while it travels from $B$ to $C$.

(iii)[3]

Calculate the power of the car’s engine as the car gets to $C$.

Worked solution & mark scheme

This 11-mark question has a full step-by-step worked solution and mark scheme. One marking point: Increase in KE $=\tfrac12\times1250(8^2-5^2)$

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