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13 June, 09:15

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 4v 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. 13 June, 10:13
    Ratio of power produced by new to old car is 16:1


    Assuming both cars have the same mass m

    Let KE1 and KE2 be the kinetic energies of the old and new car respectively.

    v1 = v

    and v2 = 4v

    KE1 = 1/2mv1² = 1/2mv²

    KE2 = 1/2mv2² = 1/2m (4v) ² = 1/2*m*16v² = 8mv²

    Ratio of the power produced by the new car to the old one is simply KE2/KE1 = 8mv²/1/2mv² = 16

    Since the same time interval is given.
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