How Far Does a Charged Particle Travel Before Stopping Due to Repulsive Force?

[Nivlac2425]

Homework Statement

A charge of -3 microC is fixed in place. From a horizontal distance of 0.045m, a particle of mass 7.2 x 10^-3 kg and charge -8 microC is fired with an initial speed of 65 m/s directly toward the fixed charge. How far does the particle travel before its speed is zero?

Homework Equations

equations of motion
Coulomb's law, to possibly find repulsive force?

The Attempt at a Solution

I tried to use Colomb's law to find the repulsive force, then F=ma to find the deceleration. After that I used equations of motion to find the distance to reach 0m/s. this didn't work, and I think it is because the repulsive force increases as the particle travels towards the fixed change.

I am stuck at how to solve this problem at this point.
Thanks everyone in advance for helping! =)

 

[LowlyPion]

The problem is that as it gets closer the field strength increases because of the decreasing distance.

But not to despair.

They give you the initial kinetic energy.

And you also know that W = q*ΔV

Figure then the change in voltage needed to overcome the kinetic energy of the particle?