Why is twice the velocity equal to four times the energy?

Question

This always puzzled me.

Answer 1

The equation for kinetic energy s:

Ek = ½*m*v²

You will see that energy is proportional to V²

Therefore if you double the velocity, the energy become 2² = 4 times.

Answer 2

Energy = depends on force x distance or mass x acceleration (distance/time^2) x distance or mass x distance^2/tine^2 or mv^2.

More formally, consider the work done by a force accelerating a body to velocity v. It comes out as 1/2 mv^2; the 1/2 arises from the integration.