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Classical Mechanics - Box sliding down a slope

  1. Feb 11, 2012 #1
    I'm on pg 56 of Thorton's Classical Dynamics book and I see this: Imgur Link

    Two questions: 1) Where does the 2 go on the second to last equation. 2) Why v0^2 and not v0 on the integral?
     
  2. jcsd
  3. Feb 11, 2012 #2

    fluidistic

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    1)[itex]\frac{d}{dt}(\dot x ^2 )=2\dot x \ddot x[/itex].
    2)I'm guessing it's because of the differential wich is a differential of velocity squared.
     
  4. Feb 13, 2012 #3
    This is bcoz
    [itex]\frac{d}{dt}(\dot x ^2 )=\frac{d}{d\dot x}(\dot x ^2 )*\frac{d}{dt}(\dot x)[/itex]
    So,[itex]\frac{d}{dt}(\dot x ^2 )=2(\dot x)(\ddot x)[/itex]
     
  5. Feb 13, 2012 #4
    This is bcoz u r integrating [itex]{d}(\dot x2)[/itex] and not [itex]{d}(\dot x)[/itex].
    So, the limits are 0 and v02.
     
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