We have two like charges(Q1, Q2) with mass (m1, m2) separated by distance (r). It is in isolation in vacuum and no other forces are acting on them.
Let it be in rest initially and we leave it to come in motion due to repulsive force between them. It is obvious that the distance between these charges will increase.
Now the problem is how to know the time taken by it to separate further by a distance (y).

I found the force and then the acceleration. But as the distance increases, repulsive force decreases, therefore acceleration decreases. So acceleration is not constant.

Question

We have two like charges(Q1, Q2) with mass (m1, m2) separated by distance (r). It is in isolation in vacuum and no other forces are acting on them.
Let it be in rest initially and we leave it to come in motion due to repulsive force between them. It is obvious that the distance between these charges will increase.
Now the problem is how to know the time taken by it to separate further by a distance (y). 

I found the force and then the acceleration. But as the distance increases, repulsive force decreases, therefore acceleration decreases. So acceleration is not constant.

anonymous · Answer

the graph for acceleration depending on the distance looks roughly like this
|dw:1337694179519:dw|
from here you can find
average acceleration = area S/(y-r0)
$$area S = \int\limits_{r_{0}}^{y}a(r)dr$$
Then you can operate the value of the average acceleration in equivalent motion with constant acceleration, and problem gets easy to solve.