[Physics] Speed of light and infinite energy

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While browsing some physics websites, I saw that to make an object reach the speed of light, it requires infinite energy and talked about its relation with Einstein's famous equation $E=mc²$. However, they didn't show how they reached the conclusion that it requires infinite energy to reach the speed of light. I would like to know how it was proved.

Best Answer

It has been observed that the momentum of an object is

$$p=\frac{m_0v}{\sqrt{1-\frac{v^2}{c^2}}}$$

So as $v$ approaches $c$, the bottom term approaches zero and therefore the momentum approaches infinity.

To increase the momentum of an object you give it additional kinetic energy. To increase the momentum infinitely takes infinite energy.

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