Past exam of the theoretical physics I course of the University of Cambridge / 2018 / 1 / c / Solution

If $e\mathbf{E}\ne 0$, then $\mathbf{p}(t)=e\mathbf{E}t+O(1)$, and the relativistic energy-momentum relation givesThe particle approaches the speed of light in the direction of the electric force, independently of its initial velocity. For positive $e$ the limiting direction is along $\mathbf{E}$; for negative $e$ it is opposite. A massive particle never reaches that limiting speed in finite time. If the force is zero, the velocity remains ${\mathbf{v}}_0$ instead.