I've been trying to work on differential equations using several books and one of the first exercise questions I encountered already has me stuck.(adsbygoogle = window.adsbygoogle || []).push({});

The momentum p of an electron at speed v near the speed c of light increases

according to the formula p=mv/√(1-v^2/c^2), where m is a constant. If an electron is subject to a constant force F, Newton's second law describing its motion is

[itex]\frac{dp}{dt}[/itex]=[itex]\frac{d}{dt}[/itex][itex]\frac{mv}{√(1-v^2/c^2)}[/itex]=F

Find v(t) and show that v → c as t→∞. Find the distance traveled by the electron

in time t if it starts from rest.

I started by taking the derivative of the momentum with respect to time and obtained:

F=ma/(1-v^2/c^2)^3/2

I'm not sure how to continue from here. This differential equation doesn't look simple to solve but it's actually from the very first set of exercises of an introductory ODE chapter so I don't think I'm actually supposed to be solving it. I think I am probably missing something that makes this really simple to solve and am confusing myself.

Any help would be appreciated.

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# Relativistic momentum problem

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