Why is kinetic energy equal to half of momentum squared over mass?

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SUMMARY

The relationship between kinetic energy (KE) and momentum (P) is established as KE = P² / 2m, where P is momentum and m is mass. This derivation is supported by integrating the expression mv dv, which leads to the standard kinetic energy formula KE = 1/2 mv². By substituting momentum in terms of mass and velocity, the equivalence of kinetic energy to half of momentum squared over mass is proven. This mathematical relationship is foundational in classical mechanics.

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tnutty
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I know that :

kinetic energy of something = P^2 / 2m , or momentum squared over 2m


why so?

I see that taking the integral of mv dv = kenitic.

can you prove this to
 
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You know p in terms of m and v. You also know E in terms of m and v. This should get you started.
 
KE = [tex]\frac{1}{2} mv ^ 2[/tex]

= [tex]\frac{1}{2} pv[/tex]

= [tex]\frac{1}{2} \frac{pmv}{m}[/tex]

= [tex]\frac{1}{2} \frac{p ^ 2}{m}[/tex]
 

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