Question

You are given that gamma=5

A) Calculate v/c

B) The non relativistic kinetic energy of a particle of mass m can be written as xmc^2 where x is a number. For gamma=5 what is x?

C) The relativistic expression is ymc^2. For gamma=5 what is y?

Answer 1

\(\begin{aligned} & \gamma=\frac{1}{\sqrt{1-\frac{v^{2}}{c^{2}}}}=5 \\ \Rightarrow & \frac{1}{1-\frac{v^{2}}{c^{2}}}=25 \\ \Rightarrow & 1-\frac{v^{2}}{c^{2}}=\frac{1}{25} \\ \Rightarrow & \frac{v}{c}=\sqrt{\frac{24}{25}} \end{aligned}\)