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Deriving Formula of Kinetic Energy using f = ma

  1. Mar 5, 2012 #1
    1. The problem statement, all variables and given/known data
    I am not fully sure where this is supposed to go, so forgive me if I get it wrong. I am just undertaking some private research and want to see if my work is correct. I wish to derive the Kinetic energy of something moving according to classical mechanics.


    2. Relevant equations
    Energy = Force * Displacement (Or distance moved).
    Force = Mass * Acceleration


    3. The attempt at a solution
    Firstly I substituted 'MA' into Energy = Mass * Acceleration * Displacement.
    Acceleration can be rewritten as Δv/Δt, and so I change my formula to be Energy = M * Δv/Δt * displacement. To find the Energy, in respect to the displacement we can make the integral ∫(M * Δv/Δt * Δd). I believe, that I can rewrite that as ∫(M * Δd/Δt * Δv), which is simply ∫(M * V * Δv). Once we solve that integral we should get the kinetic energy to be equal to E = (M * V^2)/2

    (Please point out any errors or mistakes).
     
  2. jcsd
  3. Mar 5, 2012 #2

    ehild

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    You can write Δd=VΔt, so you integral is really ∫(M * V * Δv), which is equal to 1/2 M V2 + constant.

    ehild
     
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