A particle moves in such a way that its total energy equals 4 times its rest energy. The speed of this particle is
A) 0.866c.
B) 0.968c.
C) c.
D) 0.745c.
E) c/2.

Question

Quizplus · Accepted Answer

Total energy of a particle can be expressed as $E=mc^2(\frac{1}{\sqrt{1-(v/c)^2}})$, where $m$ is the rest mass of the particle and $v$ is its velocity. 
Given $E=4mc^2$, we can rearrange to get $\frac{1}{\sqrt{1-(v/c)^2}}=4$.
Solving for $v/c$ we get $v/c = \sqrt{1-\frac{1}{16}}=\frac{3\sqrt{15}}{4}$, which is approximately equal to 0.968. Therefore, the answer is B.

A Particle Moves in Such a Way That Its Total