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Physics

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The chemical potential energy of a certain amount of gasoline is converted into kinetic energy in a truck that increases its speed from 0 mph to 30 mph. To pass another truck the driver accelerates from 30 mph to 60 mph. Compared to the energy required to go from 0 to 30 mph, the energy required to go from 30 to 60 mph is?

I say half as much?

  • Physics -

    use Energy = 0.5 mv^2
    (this should use SI units but the conversion factors will disappear in the ratio)

    at 0 the energy is 0

    at 30 the energy is =0.5xmx30^2

    the enrgy required to go from 0 to 30 is 0.5xmx30^2 - 0 = 0.5xmx30^2

    at 60 the energy is = 0.5xmx60^2

    the enrgy required to go from 30 to 60
    is 0.5xmx60^2 - 0.5xmx30^2

    which is 0.5xm(60^2 - 30^2)

    so the ratio is

    0.5xm(60^2 - 30^2)/0.5xmx30^2

    = (60^2 - 30^2)/30^2

    times as much

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