Why in E=mv^2 the kinetic energy increases to the square of the velocity???

Question

I wonder if there is an intuitive explanation for this

edit: It’s E= 1/2 m v^2 actually

In: 0

Answer 1

Well, energy is the force over distance. A faster moving object will cover more distance in the same time.

So let’s imagine an impact. An object has some energy that must be absorbed over a distance. This distance is fixed. If it is moving twice as fast, it has twice as much momentum and so you’d expect twice us much force be needed to stop it. However, it also has to dissipate this force in half as much time, so we double this yet again. Four times the force over the same distance is four times the energy for double the speed.