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Proving a known function of position via Chain Rule

  1. Jul 6, 2008 #1
    1. The problem statement, all variables and given/known data
    Use the Chain Rule to prove that for rectilinear motion, when the acceleration is a known function of position, you can find the velocity as a function of position via the integral

    [tex]\frac{v^{2}-v_{0}^{2}}{2} = \int^{s}_{s_{0}}a(s)ds[/tex]


    2. Relevant equations
    [tex]v^{2}=v_{0}^{2}\times2as[/tex]


    3. The attempt at a solution
    I took the left fraction, substituted v^2, simplified and got [tex]as[/tex]. I let A be as, then took dA to get a da. Now I'm stuck.
     
  2. jcsd
  3. Jul 6, 2008 #2
    I think you simplified wrong. It's a multipication sign not addition. See what I mean?
     
  4. Jul 6, 2008 #3
    Hold up, I wrote the question on the board wrong -- it is supposed to be a plus for the relevant equation part.
     
  5. Jul 6, 2008 #4
    I'm not exactly sure what they're asking here. For constant accelerations, you "relevant equation" is basically the answer, assuming you swap out the "x" for a "+" and take a square root. What's throwing me is the request for proof by chain rule.
     
  6. Jul 6, 2008 #5

    tiny-tim

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    Chain Rule

    Hi kylera! :smile:

    You were asked to use the Chain Rule. So …

    Hint: the LHS is ∫vdv. So use the Chain Rule on dv. :smile:
     
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