# Time velocity accelertion @ point x two electrons

If two electrons are in absolutly empty space at starting distance d1(distance between two non fixed freely moving charges) with v1 = 0(rate of change of distance between both charges)
what is v2(rate of change between both charges), a2(rate of change of rate of change of distance between both charges) at a distance d2(any distance not equal to or less than d1, being that a repulsive force is being applied) and how much time has passed I'm interested in some equation ideas :) refer to time as a function of distance I appologise for my vague wording

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Gokul43201
Staff Emeritus
Gold Member
So are we ! In fact, you should start by posting the question EXACTLY as it appears in your HW, as what you've posted is very poorly defined.

what homework I posted the last question in another subject heading and this is where they sent me literaly moved my question
I was told to rewrite my question in words thats why theres the new post I dont want specific numbers only the equations refer to time as a function of distance Im pretty sure I made a mistake but the general concept should hold true thank you for your time

I hope this looks more correct than what yall been calling garble for the past 48 hours

E(r) = (KeC^2)/r

hence

v(r) = 2keC^2/mr

t(r) = m/(2KeC^2) (1/3(r2^3) - 1/3 (r1^3)

where
r is the distance between two freely moving charges
m is the total mass of the electrons
t is time
v is the rate of change of distance between both charges

Gokul43201
Staff Emeritus
Gold Member
Let me go by what I think this is about...

At t=0, two electrons are at rest, at the origin. They are then allowed to move away from each other under their mutual electrostatic repulsion. At any time t' their posotions are x(t') and -x(t'). You want to find the value of t' for which $x(t') - \{-x(t')\} = 2x(t') = d2$

$$a(t) = \ddot {x}(t) = \frac {F(t)}{m} = \frac {kq^2}{m|x_1(t) - x_2(t)|^2}$$

$$\implies \ddot {x} = \frac {A}{x^2}$$

Solving that differential equation will give you $x(t)$, from which you can find $t(x)$ by inverting the function.

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