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Homework Help: Integral question

  1. Nov 9, 2004 #1
    say a ball falling through shampoo had a drag force of F=6.5v

    the differential equation for the objects motion is:


    to solve it, I get all of the v value on one side and integrate them:

    I know that integral[(6.5/m)(dt)] becomes 6.5t/m+c, but what will happen to the dv/v?
  2. jcsd
  3. Nov 9, 2004 #2
    How about mg ?
  4. Nov 9, 2004 #3
    ignoring the effects of gravity, sry
  5. Nov 9, 2004 #4
    the indefinite integral of dx/x is ln|x|+C

    i guess if you are looking at this as a seperable differential equation you'd have

    |v|=e^(6t/m) * e^C
    if K = +,- e^C

    i don't know, is that what you were looking for?
    Last edited: Nov 9, 2004
  6. Nov 9, 2004 #5
    [tex]\int \frac{1}{v}dv=ln |v|[/tex]
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