Question

An accelerator at a Physics Laboratory can accelerate protons to a Kinetic energy of 10 ^ 12 * eV The rest mass of a proton is m * c ^ 2 = 9.38 * 10 ^ 6 * cV . What is the speed of that proton?

Answer 1

$$E_k=\frac{mc^2}{\sqrt{1-v^2/c^2}}-mc^2$$ $$10^{12} =\frac{9.38 * 10 ^ 6}{ \sqrt{1-v^2/c^2}}-9.38 * 10 ^ 6$$

$$1-v^2/c^2=1/((E_k/mc^2+1)^2$$

$$v=c\sqrt{1-1/(E_k/mc^2+1)^2}$$

$$v=c\sqrt{1-1/(10 ^{ 12}/9.38*10^{6}+1)^2}=c$$

impossible