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Math Help - Antiderivative's application.

  1. #1
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    Antiderivative's application.

    A car is traveling at 50 mi/h when the brakes are fully applied, producing a constant deceleration of 22 ft/s^2.
    what is the distant traveled before the car comes to a stop?
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  2. #2
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    Quote Originally Posted by camherokid View Post
    A car is traveling at 50 mi/h when the brakes are fully applied, producing a constant deceleration of 22 ft/s^2.
    what is the distant traveled before the car comes to a stop?
    v' = -22 ft/s^2,

    so:

    v = -22t +v0

    at t=0 v=50*5280/60^2 ~= 73.33 ft/s

    Hence:

    v = -22 t + 73.33

    and the vehicle comes to a rest when v=0, that is when:

    -22 t + 73.33 = 0,

    or t = 3.33 s

    now if x is the distanced travelled since breaking started then:

    x' = v = -22 t + 73.33,

    so:

    x = -11 t^2 +73.33 t + x0,

    but x0=0, and at t= 3.33 s:

    x = 122.21 ft

    RonL
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