At what speed, as a fraction of c , is a particle's total energy twice its rest energy

The rest energy of a particle is

where  is the rest mass of the particle and c is the speed of light.

The total energy of a relativistic particle is

where v is the speed of the particle.

We want the total energy of the particle to be twice its rest energy, so that

which means:


From which we find the ratio between the speed of the particle v and the speed of light c:

So, the particle should travel at 0.87c in order to have its total energy equal to twice its rest energy.

Answer8.0m;