(A-level but box won't let me change it from GCSE) A particle of charge q and initial speed v is stopped by a potential difference V in distance d and time t. What was its initial momentum?

Define p=momentum, E=electric field.Firstly we know that:1) ∆p/∆t = F - definition of momentum2) F = Eq - force on particle in an electric field caused by a voltage3) E = V/d - definition of electric field of voltage V over distance dEquate F equations (1 and 2) because the force on the particle from the electric field is causing the change in momentum of the particle: 4) ∆p/∆t = EqSubstitute in E equation (3 ) to this new equation (4) so that we remove E as it is not a given quantity in the question, so we don't want it in the answer we give for initial momentum: ∆p/∆t = (Vq/d)We want initial momentum. ∆p is the change in momentum from the particle traveling at speed v to being stopped. Since when still (stopped) the particles momentum will be zero, the change in momentum (∆p) actually gives the initial momentum (p) so we can substitute in ∆p = p. Since ∆t over this event is from t=0 to t=t, we can do the same for tp/t = (Vq/d)Finally, re-arrange to get p, initial momentump = (Vqt)/d