Repelling Force with Fixed Object?

Question

If you have a repelling force in which the strength varies with the inverse square of the distance (i.e. Columb's Law for like charges), imagine having one object fixed. Then, if you have the other start some distance away from this fixed object, obviously the strength of the force diminishes as this object gets further and further away. Say you let the forces act until they get d (distance) away from each other. Is there a way to calculate the speed of the non-fixed object as we let d go to infinity?

Here is the exact wording of a problem I got:
An electron starts from rest 72.5 cm from a fixed point charge with Q=-0.125 microC (1 microC = 1 x 10^-6 C). How fast will the electron be moving when it is very far away?

The constants used are the charge on an electron is 1.60 x 10^-19 C, and its mass is 9.11 x 10^-31 kg.

Thanks in advance!

Answer 1

If the force approaches zero, then the acceleration approaches zero. Just because acceleration is zero, does NOT mean that velocity is zero.

This is an energy question, believe it or not.

KE = ½m v²
U = k q1 q2 / r


Conservation of energy implies

Ei = Ef
KEi + PEi = KEf + PEf

Initially, KEi = 0 since the particle is not moving. Finally, PEf = 0 since r = infinity, and 1/infinity = 0...

So

PEi = KEf
k q1 q2 / r = ½m v²

v = sqrt(2 k q1 q2 / m r)

Do the calculation, you should get 2.33 * 10^7 m/s.

Answer 2

I would think that as the distance approaches infinity, the force would approach 0, hence the velocity approach 0.