Derivation of Kinetic Energy

  1. Hi,

    I've always tken for granted that KE=(mv^2)/2, but never seen the derivation! I think it probably comes from U= - inegral of the force, but I can't see which force to use. Any help anyone? Maybe dimensional analysis was used?

    Thanks!
     
  2. jcsd
  3. Doc Al

    Staff: Mentor

    I suspect you are thinking of the "work-energy" theorem, in which one integrates the net force on an object over the distance traveled to obtain the change in KE.

    Start with Newton's 2nd law:
    [tex]F = m \frac{dv}{dt}[/tex]

    [tex]\int F dx = \int m \frac{dv}{dt} dx = m \int \frac{dx}{dt} dv = m \int v dv[/tex]

    I'll leave the last step to you.
     
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