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18 February, 17:08

An older-model car accelerates from 0 to speed v in a time interval of δt. a newer, more powerful sports car accelerates from 0 to 5v in the same time period. assuming the energy coming from the engine appears only as kinetic energy of the cars, compare the power of the two cars.

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  1. 18 February, 17:17
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    Power = Energy / time = Δ kinetic energy / time = ΔKE / t

    For old car: ΔKE = m (v^2) / 2 = > Power = m (v^2) / (2t)

    For new car: ΔKE = m (5v) ^2 / 2 = > Power = 25 * [ m (v^2) / (2t) ]

    Then, comparing the expressions for both cars, you get that the power of the new car is 25 times the power of the old car.
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