# Ultrarelativistic limit

Einstein then went on to show that a particle can never achieve the speed of light, because you get a divide by zero error from the equation for kinetic energy, $E_k = m_0 ( \gamma -1 ) c^2 = \frac{m_0 c^2}{\sqrt{1-\frac{v^2}{c^2}}} - m_0 c^2,$. Look at the denominator (bottom) of the equation, ${\sqrt{1-\frac{v^2}{c^2}}}$. "v" refers to the velocity of the particle. If its velocity reaches the speed of light (which is "c" in this equation), $\frac{v^2}{c^2}$ will equal one, and since that would leave one minus one in the denominator, there would be a divide by zero error.