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

Energy, work and power — practice question

A resisting force of magnitude $1400\text{ N}$ acts on a car whose mass is $1250\text{ kg}$.
(a)[2]

The car is travelling in a straight line on a horizontal road at a steady speed of $28\ \text{m\,s}^{-1}$. Determine, in $\text{kW}$, the rate at which the engine is operating.

(b)[3]

The car then moves up a hill at constant speed on a slope making an angle of $\theta$ with the horizontal, where $\sin\theta = 0.12$, while the engine works at $43.5\ \text{kW}$. Determine this speed.

(c)[4]

At a different time, the car tows a trailer of mass $600\,\text{kg}$ up the same hill. The car and trailer are represented as particles joined by a light inextensible cable. The engine of the car provides a driving force of $5000\,\text{N}$, and the resistance opposing the trailer’s motion is $300\,\text{N}$. The resistance opposing the car’s motion is still $1400\,\text{N}$. Determine the acceleration of the system and the tension in the cable.

Worked solution & mark scheme

This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: Thus, Power $= 1400\times28$

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