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After brakes are applied how far does the car travel? - integrating twice

  1. Sep 9, 2010 #1
    1. The problem statement, all variables and given/known data
    t seconds after the brakes of a car are put on, the acceleration of the car is a(t) = -6t - 4 ft/sec^2. If the automobile was moving at the speed of 32 ft/sec when the brakes were put on, how far does it go before stopping?

    2. Relevant equations
    a(t) = -6t - 4 ft/sec^2

    3. The attempt at a solution

    integral of a(t) = -6t - 4 ft/sec^2 ----> |-3t^2 - 4t + c| = 32
    I put the absolute value because it is the speed. is that right?

    v(0) = c = 32

    v(t) = -3t^2 -4t + 32

    -3t^2 -4t + 32 = 0
    t = 8/3

    integral from 0 to 8/3 of -3t^2 -4t + 32

    = 52.1481 ft

    The main thing I am worried about is that it says speed instead of velocity, can anyone help me out here? Thanks! :)
  2. jcsd
  3. Sep 9, 2010 #2


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    Homework Helper

    That should be correct what you did.

    But you don't need the modulus sign really.
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