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Derivation of Kinetic Energy 
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#1
Feb1806, 05:38 AM

P: 5

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
Feb1806, 06:29 AM

Mentor
P: 41,578

I suspect you are thinking of the "workenergy" 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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