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.

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