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Derivative of the kinetic energy

  1. Feb 10, 2008 #1
    Derivative of the kinetic energy....

    1. The problem statement, all variables and given/known data
    If you take the derivative of the kinetic energy of a particle with respect to its velocity you get...
    A) force
    B) momentum
    C) acceleration
    D) mass
    E) potential energy

    2. Relevant equations
    K= .5mv^2

    3. The attempt at a solution
    Im in pre calc right now and i have no idea how to take the derivative of anything, quick google searching led me to believe that its a calculus thing, so it would be really helpfull if someone could explain how to do this..
  2. jcsd
  3. Feb 10, 2008 #2


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    Homework Helper

    If you have


    and you want to find the derivative of that with respect to x,denoted as [itex]\frac{dy}{dx}[/itex]

    it is simply


    Where k is a constant
  4. Feb 10, 2008 #3
    I think the answer is B momentum, is that right? momentum has p=mv and kinetic energy has the same variables, so it must be B right?
    Also K=mv^(2-1) would be the same as K=mv which is the the same as momentum, is this correct?
  5. Feb 10, 2008 #4


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    Homework Helper

    [tex]\frac{dK}{dv}=mv[/tex] which is momentum so you are correct.
  6. Feb 10, 2008 #5
    You could also exploit the notation and think about it in terms of units.

    [tex]dK/dv = [\frac{kg * m^2/s^2}{m/s}] = [kg * m/s][/tex]
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