Originally Posted by **avito009** I was noticing that there is a lot of similarity between the formula of kinetic energy 1/2 mv2 and Einstein's E=mc2. Was Einstein inspired from this kinetic energy formula when he came up with E=mc2? |

The short answer is "no."

The longer answer is that $\displaystyle E = mc^2$ (where m is the rest mass, sometimes written as $\displaystyle m_0$) is only true for an object at rest. The full equation for a moving object is $\displaystyle E^2 = (mc^2)^2 + (pc)^2$, where p is the momentum of the object. The total energy, E, can also be shown to be $\displaystyle E = \gamma ~ mc^2$, where I have defined $\displaystyle \gamma$ below.

The formula for kinetic energy in Special Relativity is $\displaystyle E = ( \gamma - 1)mc^2$. To make contact with non-relativistic theories we can expand the $\displaystyle \gamma = \frac{1}{\sqrt{1 - \left ( \frac{v}{c} \right ) ^2}}$ for v << c which gives

$\displaystyle KE = ( \gamma -1 )mc^2 = \left ( \frac{1}{\sqrt{1 - \left ( \frac{v}{c} \right ) ^2}} - 1 \right ) mc^2 \approx \frac{1}{2} mv^2 + \frac{3}{8} m \frac{v^4}{c^2} + \text{ ...}$

You can see that the largest term is the usual kinetic energy and that the extra terms are fairly small and can be ignored for Classical Physics.

-Dan