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Derivatives problem help

  1. Nov 1, 2005 #1
    Hello can someone point in the right direction on this one.

    A particle moves along a strainght line with displacement s(t), velovity v(t), and acceleration a(t). Show that

    a(t) = v(t) dv/ds

    Explain the difference between the meanings of the derivatives dv/dt and dv/ds.

    Does dv/dt mean differance of velocity over the differance time ?

    Does dv/ds mean differance of velocity over the differance displacement ?

    Any help would be great? Thanks
     
  2. jcsd
  3. Nov 1, 2005 #2

    HallsofIvy

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    Science Advisor

    Basically yes: how fast the speed changes "per foot" rather than "per second", for example.
    To do the first part, use the chain rule:
    [tex]\frac{dv}{dt}= \frac{dv}{ds}\frac{ds}{dt}[/tex]
     
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