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The electric motor of a model train accelerates the train from rest to 0.680 m/s in 23.0 ms. The total mass of the train is 580 g. Find the average power delivered to the train during its acceleration.

  • physics -

    power = work / time

    work = force x distance

    force = mass x acceleration

    acceleration and distance can be calculated by....

    Vf = Vo + at -----> a = (Vf -Vo) / t = Vf/t

    and

    d = Vot + 1/2 at^2 = 0 + 1/2 * (Vf/t) * t^2 = 1/2 * Vf * t

    so....

    power = mass x acceleration x distance / t
    = m * a * d / t = m * (Vf/t) * (1/2 Vf t) /t = m Vf^2 / (2t)
    = 580 g * (.664 m^2/s^2) / (2 * 17 * 10^-3 s) = 17.094 (kg m^2/s^2) / s = 17.094 Joule / sec = 17.094 watts

    = 17.1 watts

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