# What is the Difference Between Energy & Kinetic Energy?

The energy of matter is $mc^2$ where $m$ is the mass of the matter and $c$ is the velocity of light. We consider an example of a Newtonian system accelerating a mass $m$ from zero to velocity $v$, where $v \ll c$. The energy given up by the Newtonian system is $mv^2$. We also show that the work done by the accelerating system is half the energy given up by the accelerating system.

We know that the energy of matter is $mc^2$, i.e., its mass times the square of velocity. We say that a ball of mass $m$ translating at velocity $v$ has a kinetic energy of $\frac{1}{2} {mv^2}$. But, isn’t its energy $mv^2$? We think so. How do we reconcile the fact that the work, i.e. energy expended, which is $\int F dx$ required to bring the energy of the ball up to $mv^2$, when only half that amount of work is required?

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What is the Difference Between Energy and Kinetic Energy