math

The stopping distance d of a car after the brakes have been applied varies directly as the square of the speed r. If a car traveling 40 mph can stop in 100 ​ft, how fast can a car travel and still stop in 256 ​ft?

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  1. Just translate ...

    d = k(r^2) , where k is a constant
    plug in the given to find k

    100/5280 = k(1600)
    k = (100/1600)/(5280) = 1/84480

    so your formula is
    d = (1/84480)r^2
    if d = 256 ...
    256/5280 = (1/84480)r^2
    84480(256)/5280 = r^2

    256(16) = r^2

    r =16(4)
    = 64 mph

    notice we could have skipped the 5280 ft to mile conversion, since in both cases the same units were used. e.g. mph <---> ft

    .........................

    we could have used a simple ratio:

    d1/d1 = (r1)^2/(r2)^2

    100 ft/256 ft = (40 mph)^2/ (r2)^2
    25/64 = 1600/r2^2
    take √ of both sides
    5/8 = 40/r2
    5r2 = 320
    r2 = 64

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  2. Where does the 5280 come from?

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