Question

At what speed, as a fraction of c, is a particle's kinetic energy twice its rest energy? Express your answer using three significant figures. v=

Answer 1

the relation between kinetic energy and rest energy is

$KE = (\frac{1}{\sqrt{1-\frac{v^{2}}{c^{2}}}}-1) * E$

here it is given KE = 2 * E

so $(\frac{1}{\sqrt{1-\frac{v^{2}}{c^{2}}}}-1) = 2$

$\frac{1}{\sqrt{1-\frac{v^{2}}{c^{2}}}}=3$

$1-\frac{v^{2}}{c^{2}}=\frac{1}{9}$