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Implicit Integration?

  1. Jan 31, 2016 #1
    • Member warned about posting with no effort shown
    1. The problem statement, all variables and given/known data
    Integrate
    $$v = \sqrt{2g\frac{T-v \pi r^2t}{\pi R^2}}$$

    where g,T,r,R are constants

    2. Relevant equations
    N/A

    3. The attempt at a solution
    I tried playing around with the variables, but I am not sure how to integrate this. Just give me a little bit of hint would do. Thanks!
     
  2. jcsd
  3. Jan 31, 2016 #2

    Ray Vickson

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    Integrate what? Are you solving for ##v##as a function of ##r## or ##t## for example, then calculating ##\int v\, dr## or ##\int v\, dt##? Or, are you solving for (say) ##r## as a function of ##v## then computing ##\int r \, dv##? Or are you trying to do something else?
     
  4. Jan 31, 2016 #3
    I sincerely apologize for my lack of explanations.

    v is velocity and t is time. The rest are just constants. I want to integrate velocity vs. time to find the displacement equation
     
  5. Jan 31, 2016 #4

    Ray Vickson

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    It will be messy. Just solve for ##v## as a function of ##t## (I.e., ##v = f(t)##) then integrate, or try to. You will get a quadratic equation in ##v##, so there will be two roots (that is, two functions ##v = f_1(t)## or ##v = f_2(t)##) and you will need to figure out which one is the correct root, probably using other information that you have.
     
  6. Jan 31, 2016 #5
    Thank you very much, I think I have a basic understanding now! Very appreciate it!
     
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