2-d kinematic w/non-constant acceleration

[rjs123]

Homework Statement

I'm not sure how to set up the differential equation. I've got 2 point charges...both positive. One charge is fixed in position (0, -250m)...the other is traveling at an initial speed in the -x direction (10,000m, 0) with 0 acceleration. At time t=0, I calculated the force applied in the x and y direction on the moving charge...I know the acceleration, velocity, and position after 1 second using Newton's motion equations. The acceleration and force is non-constant in this situation...it starts at say -5 m/s^2 and then at say t=8 seconds will be at -60 m/s^2...then at t=9...the force in the x-direction will decrease... and then the acceleration will start dropping...-55 m/s^2 and so on. This transition happens before the moving charge crosses the origin.

Any help appreciated...thanks.

Differential equation will involve:

F = ma

a = dv/dt

I don't know how to set it up after this.

 

[Uniquebum]

So the force applied is tied to the position of the particle? Unless you know how it's tied to the position, it's pretty much impossible to create the equation. The info you gave is a bit messy. Try to simplify/clean it up a bit.

 

[rjs123]

yes, the force applied depends upon its position since we are dealing with electromagnetic force. It seems without an equation given...I would have to calculate the variables separately per second, which won't be as accurate.