How Is the Formula for Kinetic Energy Derived?

[francescopadormo]

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!

 

[Doc Al]

I suspect you are thinking of the "work-energy" 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:
$$F = m \frac{dv}{dt}$$

$$\int F dx = \int m \frac{dv}{dt} dx = m \int \frac{dx}{dt} dv = m \int v dv$$

I'll leave the last step to you.