Kinetic energy

Kinetic energy is the energy of motion, defined as the amount of work needed to accelerate an object from rest to its current velocity.

In classical mechanics, kinetic energy is given by:


 * $$E = \frac{1}{2}mv^2$$

where $$m$$ is the mass of the object. However, this formula does not take into account the fact that as an object approaches the speed of light, it takes more and more energy to accelerate, such that the speed of light can never be reached. This is taken into account by the theory of relativity, which restates the formula as:


 * $$E = \left(\gamma-1\right)mc^2 = \gamma mc^2 - mc^2$$

When we substitute in the definition of $$\gamma$$, we get:


 * $$E = \frac{mc^2}{\sqrt{1-\frac{v^2}{c^2}}} - mc^2$$