Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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

    User Avatar
    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]
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook