Displacment equation of a charged particle

[thetrice]

In a case of a charged particle attracted to another fixed chrged particle both on one axis.
force on charged particle will be F= (const)(q1*q2)/(r^2)
for simplification = q1*q2*const =1 , and also mass of particle will be equal to one .
so acceleration = 1/(r^2)
r is distance between 2 particles, Another simplification is to assume r = X which is displacemnt of chrged particle(assuming fixed particle at fixed cordinates of(0,0,0) .
so equation is accelration=1/(x^2)
where x= velocity*time , velocity = initial velocity + acceleration *time.
so how can i get displacement in variable of time ?
Problem is that X is affected by v , v is affected by a , and a is affected by X. so its a loop.

 

[Simon Bridge]

In a case of a charged particle attracted to another fixed chrged particle both on one axis.
force on charged particle will be F= (const)(q1*q2)/(r^2)
for simplification = q1*q2*const =1 , and also mass of particle will be equal to one .
so acceleration = 1/(r^2) r is distance between 2 particles, Another simplification is to assume r = X which is displacemnt of chrged particle(assuming fixed particle at fixed cordinates of(0,0,0) .
so equation is accelration=1/(x^2)
where x= velocity*time , velocity = initial velocity + acceleration *time.
so how can i get displacement in variable of time ?
Problem is that X is affected by v , v is affected by a , and a is affected by X. so its a loop.

Putting both charges on the x axis...
You need to solve:

\frac{d^2x}{dt^2} = \frac{1}{x^2}