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Math Help - Car stopping distance

  1. #1
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    Car stopping distance

    Well, I failed my driving permit test because of this one question...

    If a car is going at 10mi per hour with a stopping distance of 20 feet. If the car was going 20 miles per hour how far would the stopping distance be?

    Well here were the choices

    20 - knew this was wrong
    40 - chose this
    6x - I was deciding this between 40 and 60
    7x - I considered this way off.

    How did I get this wrong?
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  2. #2
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    skeeter's Avatar
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    double the speed ... the stopping distance is quadrupled.
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  3. #3
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    e^(i*pi)'s Avatar
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    When a car brakes all it's kinetic energy must be lost as heat. Since kinetic energy is proportional to the square of the speed/velocity doubling the speed will quadruple the stopping distance:

    E_{k1} = kv^2

    E_{2k1} = k(2v)^2 = 4kv^2

    \frac{E_{2k1}}{E_{k1}} = \frac{4kv^2}{kv^2} = 4
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