From a large distance away, a particle of mass $m_{1}$ and positive charge $q_{1}$ is fired at speed $v$ in the positive $x \mathrm{di}-$ rection straight toward a second particle, originally stationary but free to move, with mass $m_{2}$ and positive charge $q_{2} .$ Both particles are constrained to move only along the $x$ axis. (a) At the instant of closest approach, both particles will be moving at the same velocity. Find this velocity. (b) Find the distance of closest approach. After the interaction, the particles will move far apart again. At this time, find the velocity of (c) the particle of mass $m_{1}$ and (d) the particle of mass $m_{2}$.