- #1
Pual Black
- 92
- 1
Homework Statement
At what speed the kinetic energy of particle equal n times it's rest energy
Homework Equations
i use this equation
##T=(\gamma - 1)m_{0}c^{2} ##
The Attempt at a Solution
##T=n(m_{0}c^{2})##
##n=\gamma -1##
##\gamma =n+1##
##\frac{1}{\sqrt{1-\frac{v^{2}}{c^{2}}}}=n+1##
##\frac{1}{1-\frac{v^{2}}{c^{2}}}=n^{2}+2n+1##
##\frac{1}{n^{2}+2n+1}=1-\frac{v^{2}}{c^{2}}##
##\frac{v^{2}}{c^{2}}=1-\frac{1}{n^{2}+2n+1}##
##\frac{v^{2}}{c^{2}}=\frac{n^{2}+2n+1-1}{n^{2}+2n+1}##
##v=\sqrt{\frac{n^{2}+2n}{n^{2}+2n+1}} ~~ c##
this is what i get.
Is that correct? isn't there
other solution?