For the image below, lets say the top charge is 5C and the bottom 1C. And consider this observation frozen at $t=0$, consider an imaginary horizontal line between the 2 charges denoting the centre of the distance between them They both exert the same equal and opposite forces on each other, equal and opposite forces imply no acceleration of change in velocity. Unfrozen at $t=1$, from $t=1$ to $t=2$ do both charges move the same distance from this horizontal line assuming the mass of both are the same?
dictates that the force felt by each of the two charges is equal. Given that their masses are equal and $F=ma$, this also means their accelerations are equal, and thus their distance from the horizontal line will be the same, as a function of time.