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

[tnutty]

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

 

[Vanadium 50]

You know p in terms of m and v. You also know E in terms of m and v. This should get you started.

 

[dE_logics]

KE = $$\frac{1}{2} mv ^ 2$$

= $$\frac{1}{2} pv$$

= $$\frac{1}{2} \frac{pmv}{m}$$

= $$\frac{1}{2} \frac{p ^ 2}{m}$$