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Acceleration function of velocity example

  1. Sep 20, 2012 #1
    1. The problem statement, all variables and given/known data

    Because the drag on objects moving through air increases as the square
    of the velocity, the acceleration of a bicyclist coasting down a slight hill
    is (v) = a - cv where a and c are constant. Determine the velocity of
    the bicyclist as a function of distance if the velocity is zero when x=0.
    Also determine the maximum velocity that the cyclist attains.


    2. Relevant equations
    dx/dt = v
    dv/dt = a-cv

    3. The attempt at a solution
    x = -v/c - (a/c^2)*ln(a-cv)/a
    v = (a - ae^-ct)/c
    t = -(cx + v)/a = -(1/c)*ln(a-cv)/a
     
    Last edited: Sep 20, 2012
  2. jcsd
  3. Sep 21, 2012 #2
    "...the acceleration of a bicyclist coasting down a slight hill
    is (v) = a - cv where a and c are constant."

    Shouldn't the v on LHS be dv/dt?

    Hint for v as a function of distance:

    V = dx/dt = (dx/dv)*(dv/dt) = (dx/dv)*(a - c*V)

    Maximum velocity occurs when acceleration is zero. which is what your second equation shows for large t.
     
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