## College Physics (4th Edition)

The acceleration is less than $\frac{F}{m}$
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 find an expression for the acceleration: $F = m_{rel}~a$ $a = \frac{F}{m_{rel}}$ $a = \frac{F}{\frac{m}{\sqrt{1-\frac{v^2}{c^2}}}}$ $a = \frac{F~\sqrt{1-\frac{v^2}{c^2}}}{m} \lt \frac{F}{m}$ The acceleration is less than $\frac{F}{m}$.