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May/June 2026 p42 q1
4335
A car of mass \(960\text{ kg}\) is moving on a straight horizontal road. There is a constant force of magnitude \(620\text{ N}\) resisting the motion of the car.
(a) Calculate the power developed by the engine of the car when it is moving at a constant speed of \(25\text{ m s}^{-1}\).
(b) Given that the power is suddenly increased by \(12\text{ kW}\), find the instantaneous acceleration of the car.
Solution
✔ Checked by expert
(a) When the car moves at constant speed, the driving force is equal to the resisting force.
\[
F=620\text{ N}.
\]
Power is given by
\[
P=Fv.
\]
So
\[
P=620(25)=15500\text{ W}.
\]
\[
P=15.5\text{ kW}.
\]
Answer: \(15.5\text{ kW}\).
(b) The new power is
\[
15.5+12=27.5\text{ kW}=27500\text{ W}.
\]
At the instant the power is increased, the speed is still \(25\text{ m s}^{-1}\).