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A car of mass $1200 \mathrm{~kg}$ (together with the driver) is moving with a constant acceleration of $2 \mathrm{~m} / \mathrm{s}^2$. How much power does the engine generate at the instance, when the speed reaches $20 \mathrm{~m} / \mathrm{s}$ ? (Assume that the coefficient of friction between the car and the road is 0.5 ).
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Verified Answer
The correct answer is:
$168000 \mathrm{~W}$
Power of engine overcomes friction and provides necessary acceleration to the car.
Now friction, $f=\mu m g=0.5 \times 1200 \times 10=6000 \mathrm{~N}$ and accelerating force, $F=m a=1200 \times 2=2400 \mathrm{~N}$ So, total force produced by engine
$$
=F_T=8400 \mathrm{~N}
$$
We know that, the formula of power is
$$
P=F_T v
$$
Then, $P=8400 \times 20=168000 \mathrm{~W}$
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