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Homework Help: Finding displacement from variable acceleration

  1. Mar 14, 2012 #1
    Hello, I've been staring at this question for an hour with no luck.. if anyone could point me in the right direction that would greatly appreciated!

    1. The problem statement, all variables and given/known data

    a = acceleration
    v = velocity
    x = displacement
    m and n are constants
    vt = terminal velocity

    Show that after travelling x, car will have velocity v.

    2. Relevant equations

    a = m - nv2 <- given equation

    and vt = sqrt(m/n)

    x = -0.5ln(1 - (v/vt)2) <- equation need to find

    3. The attempt at a solution

    I have attempted to substitute in a = d/dx(0.5v2) and then integrate with respect to x but had no luck.

    Am stuck with where to go next! Any help would be greatly appreciated!
  2. jcsd
  3. Mar 14, 2012 #2


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    Science Advisor
    Homework Helper

    Welcome to PF!

    Hello TPHughes! Welcome to PF! :smile:
    vdv/(m - nv2) = dx :wink:
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