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An older-model car accelerates from 0 to speed v in a time interval of $∆ t .$ A newer, more powerful sports car accelerates from 0 to 2v in the same time period. Assuming the energy coming from the engine appears only as kinetic energy of the cars. Choose correct statement.

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The power of the sports car is equal to that of the older-model car.

The power of the sports car is four times that of the older-model car.

The power of the sports car cannot be compared from given data.

The power of the sports car is two times that of the older-model car.

answer is A.

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Detailed Solution

P = $\frac{W}{∆ t}$

older-model: W = $\frac{1}{2} {mv}^{2} \Rightarrow P_{older} = \frac{\frac{{mv}^{2}}{2}}{∆ t} = \frac{{mv}^{2}}{2 ∆ t}$

newer-model: $W = \frac{1}{2} m {(2 v)}^{2} = \frac{1}{2} (4 {mv}^{2})$

$\to P_{never} = \frac{4 {mv}^{2}}{2 ∆ t} = 4 \frac{{mv}^{2}}{2 ∆ t}$

Hence the power of the sports car is four times that of the older-model car.

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