This refers to problem 1-16 in Special Relativity by A. P. French.

Problem: An electron is accelerated through a voltage $V$ so that its mass increases by $f=0.4\%$. (a) Through what voltage was the electron accelerated? (b) What is the speed under these conditions?

Solution Let $m_e$ denote the electron rest mass, $\gamma$ the Lorenz factor $\gamma = m/m_e = 1+f$. Recall

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

Solving for $v$,

$$ v = c\sqrt{1-1/\gamma^2} \approx 0.089c $$

This solves (b). Now we return to (a). We have $Vq_e=KE=(\gamma-1)E_0=fE_0$. Thus $V=fE_0/q_e=fm_e c^2/q_e$. According to Mathematica, this works out to about $2.04\ k\mathrm{V}$.