Question

At what speed is a particle's kinetic energy twice its rest energy?

Answer 1

The total energy of a particle is its rest energy plus the kinetic energy. Its formula is: Et= m^2/sqrt((1-v^2)/c^2))
The rest energy is equal to the product of mass and the square of light velocity: Er=mc^2.
When the kinetics energy is twice its rest energy this holds:
Et=Er
m^2/sqrt((1-v^2)/c^2))=mc^2.
sqrt((1-v^2)/c^2))=m/c^2
=> v=sqrt(3/2)c