Chapter 8.1, Problem 7P

The momentum $p$ of an electron at speed $v$ near the speed $c$ of light increases according to the formula $p=mv/\sqrt{1-v^2/c^2},$ where $m$ is a constant (mass of the electron). If an electron is subject to a constant force $F$, Newton’s second law describing its motion is $\begin{array}{ll}\hfill & \frac{dp}{dt}=\frac{d}{dt}\frac{mv}{\sqrt{1-v^2/c^2}}=F\hfill \end{array}$.

Find $v(t)$ and show that $v\to c$ as $t\to \infty .$ Find the distance traveled by the electron in time $t$ if it starts from rest.