When a charged particle is accelerated through a potential difference, the work done by the electric field appears as kinetic energy of the particle (Work-Energy Theorem) [Source 30, 73].

1. Work Done: The work done ($W$) on a charge $e$ moving through a potential difference $V$ is given by $W = eV$ [Source 153].
2. Kinetic Energy: This work is converted into the kinetic energy ($K$) of the electron. Since it starts from rest, the final kinetic energy is $K = \frac{1}{2}mv^2$.
3. Conservation of Energy: Equating work done to the gain in kinetic energy: $eV = \frac{1}{2}mv^2$
4. Solve for velocity ($v$): $v^2 = \frac{2eV}{m}$ $v = \sqrt{\frac{2eV}{m}}$ [Source 47].