As the other charge particle exerts force on the charge Q, the external agent has to apply equal and opposite force to keep it stationary. This force is thus equal to the force exerted on q by Q.
Net impulse is I=∫t0Fdt=mΔ→vq
Initial Potential energy q is Ui=14πϵ0Qqr
Final Potential energy of q is Uf=14πϵ0Qq2r
As the charge q is only under the influence of electrostatic forces, mechanical energy is conserved.
Final Kinetic energy id Kf=Ui−Uf=14πϵ0Qq2r
Thus, vq=√2Kfm⇒I=mvq=√2mKf=√Qqm4πϵ0r