A charged particle with charge q is accelerated from rest by a uniform time independent electric field E.
(a) Derive an equation of motion for the velocity v of a relativistic particle that is accelerated by a uniform time-independent electric field E. Hint: remember that both the relativistic momentum p and the relativistic γ are going to be changing during the acceleration.
(b) Calculate the velocity as a function of the elapsed time t in the laboratory reference frame. Note: you may not necessarily need to use the result of (a) to do this calculation.
(c) If the acceleration was going on over a period of time 0 < t < T in the laboratory frame, how much time elapsed in the particle's reference frame?