Question

What is kinetic energy of relativistic particle.

Answer 1

Total energy of the particle consists of rest energy and kinetic energy. The total relativistic energy of the particle is

$E = \gamma mc^2$

where $\gamma$ is Lorenz factor.

The rest energy is $E_0 = mc^2$. So kinetic energy is

$E_k = E - E_0 = \gamma m c^2 - mc^2 = mc^2 (\gamma -1)$