I’m trying to solve the following problem for a long time:(adsbygoogle = window.adsbygoogle || []).push({});

There are two charged particles, one doesn’t move, the other is being accelerated and is initially at rest, I would use the particle that doesn’t move as the referential, this referential has only one dimension, how do I find the position as a function of time.

I tried this approach, by Coloumb’s law the force in the second particle is F=(k*q*Q)/r^2, for simplification I put a C in place of k*q*Q, now I use Newton’s second law, I get a=C/(m*x^2), then I try to put velocity as a function of time, so the work done on the particle as a function of the distance is found by solving the integral of the force as a function of the distance between x and x0(this is the initial position), I got W=(c/x)-(c/x0), knowing that the particle starts at rest, its kinetic energy must be equal to the work done by the electrical force so W=(mv^2)/2, I put velocity as a function of the position, that is v=√((2c/(xm))-(2c/(x0m))), now the idea of all this stuff was to use the relation a=dv/dt to get the position as a function of time, this is what I don’t know how to do and would appreciate someone’s help in solving the problem this way or a different propose for a solution.

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# Distance dependent force

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