to solve this problem we will need to apply integration so better learn the concept as the same question is also asked in mechanics as well

initially the seperation is 10 cm let the separation at any instant be x

the force at that moment is

F = K * q²

              x²

and accordingly the accelaration is force divided by mass

now

let us say that the velocity at that instant is v

and in a displacement of dx the accelaration is nearly the same

and final velocity becomes v + dv

now consider

(v + dv)² - v²  = 2 * a *d x

=> v² + dv² + 2*v*dv - v² = 2*a*dx

=>  2 * v * dv  = 2 * kq²/mx²* dx    (neglectin dv² because it will be a very small quantity)

the same result can be obtained by differentiation also

now once you get the above eqn

integrate it with

v varying from  0 - v

and x varying from 10cm to infinty (and since x is in denominator the term will amount to zero)

the integration is simple

v² - 0 = 6 kq²/(m * (10 cm)³) - 0

plug in k q and m

and calculate v