How Fast Do Charged Particles Move When Halving Their Initial Separation?

[nutster]

Here's the problem:
Two particles each have a mass of 6.6x10^-3 kg. One has a charge of +5.0x10^-6 C, and the other has a charge of -5.0x10^-6 C. They are initially held at rest at a distance of 0.70 m apart. Both are then released and accelerate toward each other. How fast is each particle moving when the separation between them is one-half its initial value?


I've tried a couple of different ways to attack this, with this one making the most sense to 'me' :

Knowing both charges and the distance between them, I applied Coulomb's Law to determine a force of .459 (maybe this is my problem? One charge has to remain stationary..?)

I then applied this to Newton's F=ma, which would yield an acceleration of 69.49 m/s/s. I finally applied this to Kinematics and found the final velocity after 0.175m (the distance each particle traveled after a combined 0.30 m change in distance).


So...where'd it all go wrong? I doubt I'm attacking this the right away, so any thoughts are appreciated :)

Thanks.

 

[Astronuc]

Try approaching it from conservation of energy.

Initially, there is a potential energy of some amount with the charges at some separation, and the total kinetic energy is 0.

Then calculate the potential energy when they are at half the distance. The change in potential energy should equal the resulting kinetic energy - assuming no losses due to radiation.

 

[nutster]

I don't understand where we're going with EPE Might you be able to provide equations to show what you mean?

Thanks again