When two like charges are held together , they have EPE = kQ1Q2/r.
If one is allowed to move and the other fixed in its position , the PE will be converted to kinetic energy. Equate EPE = KE. You can find the speed of the get away charge!
An alpha particle projected towards the gold nucleus is a similar problem where energy exchange from KE to EPE. Find the closest distance of approach r if speed of alpha is given .1/2mv2 = kQ1Q2/r , find r.
If two like charges and equal mass move apart , then the formuala is