## College Physics (4th Edition)

We can write an expression for the relativistic mass of an object when it is moving at speed $v$: $m_{rel} = \frac{m}{\sqrt{1-\frac{v^2}{c^2}}}$ We can write an expression for the momentum: $p = m_{rel}~v$ We can write an expression for the kinetic energy: $K = \frac{1}{2}~m_{rel}~v^2$ We can see that as $v$ gets closer to $c$, the value of $m_{rel}$ increases without any upper limit. Therefore, momentum and kinetic energy do not have any maximum value.