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Integration to find velocity

  1. Feb 10, 2010 #1
    1. The problem statement, all variables and given/known data
    I intend to use the Runge-Kutta method but to do so I need to be able to find the velocity [tex]\frac{dx(t)}{dt}[/tex] from the acceleration and I need some pointers on how to get that from the equation below. In other words I am having difficulty integrating the equation wrt time.

    2. Relevant equations
    [tex]\frac{d^{2}x(t)}{dt^{2}} = \frac{k}{x(t)^{2}}[/tex]

    where k is a constant.

    Any help would be appreciated. Thank-you.
  2. jcsd
  3. Feb 10, 2010 #2


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    I don't think you can express the velocity in any easy form. Isn't the usual trick to add dx(t)/dt=v(t) to your list of equations and make the first equation dv(t)/dt=k/x(t)^2 and solve that first order system of equations with Runge-Kutta?
  4. Feb 10, 2010 #3
    dont you need x(t)²??
  5. Feb 10, 2010 #4
    The problem is Runge-Kutta method uses two variables, in my case x and t, though at the moment I only have 1 variable x as expressed in the equation of acceleration.
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