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Homework Help: Finding velocity as a function of time

  1. Feb 27, 2012 #1
    Okay so the problem is that we have the case of a ball being thrown up at initial velocity v° with air resistance expressed as F = -kv where k is a constant acting on it. We are suppose to find a differential equation for the velocity at a given point as a function of time. So I started with
    ƩF = ma
    - mg - kv = ma

    Then I moved everything around to get
    dv/dt = (-mg - kv)/m

    Now we have never done a solution like this in my AP Physics class so I am rather at a lose. I know that I need to get it so that dv and v are on the same side but I'm not really sure how to go about that so that I can integrate the whole equation to get the solution.
  2. jcsd
  3. Feb 27, 2012 #2
    Try inversing both sides
  4. Feb 27, 2012 #3
    How would I find the inverse of dv/dt we have never done something like that before.
  5. Feb 28, 2012 #4


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    Homework Helper

    Take the kv term over to the other side. Multiply both sides by dt. Integrate.
    You will need to remember that the integral of v*dt is distance. It works out nicely this way. I don't understand the inverse method.
  6. Feb 29, 2012 #5
    You inverse both sides to get dt/dv = m/(-mg - kv) and then multiply both sides by dv
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