When two charged particles move toward each other and come to a stop due to their mutual electric repulsion (if they have the same charge) or attraction (if they have opposite charges), the behavior afterward depends on their charge and the context.
If they have like charges, they will repel each other and will accelerate in opposite directions. If they have opposite charges, they would attract each other, and after stopping, they would start to accelerate toward each other again. However, since the question does not specify the charge of the particles, the safest general response is:
They accelerate in opposite directions.