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Math Help - Antiderivative's application2

  1. #1
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    Antiderivative's application2

    A car braked with a constant deceleration of 16ft/s^2, producing a marks measuring 200ft before coming to a stop.
    How fast was the car traveling when the brakes were first applied?
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  2. #2
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    Quote Originally Posted by camherokid View Post
    A car braked with a constant deceleration of 16ft/s^2, producing a marks measuring 200ft before coming to a stop.
    How fast was the car traveling when the brakes were first applied?
    Let the initial speed be v0, then under braking we have:

    v' = -16 ft/s^2

    so:

    v = -16 t + v0

    and so the vehicle comes to rest at t=v0/16 s.

    Now let x be the distance travelled since braking started then:

    x' = v = -16 t + v0

    so:

    x = -8 t^2 + v0 t + x0,

    but x0=0 here so:

    x = -8 t^2 + v0 t

    As the vehicle stops after 200ft we know that:

    200 = -8 (v0/16)^2 + v0 (v0/16)

    simplifying gives v0^2 = 6400, and so v=80 ft/s

    RonL
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