This isn't a homework question, simply one I found in a book that I'm trying to do:(adsbygoogle = window.adsbygoogle || []).push({});

momentum p, of electron at speed v near speed of light increases according to formula

p = [tex]\frac{mv}{\sqrt{1 - \frac{v^{2}}{c^{2}}}}[/tex]

if an electron is subject to constant force F, Newton's second law of describing motion is

[tex]\frac{dp}{dt}[/tex] = [tex]\frac{d}{dt}[/tex] [tex]\frac{mv}{\sqrt{1 - \frac{v^{2}}{c^{2}}}}[/tex] = F

This all makes sense to me. It then says, find v(t) and show that v --> c as t --> infinity. Find the distance travelled by the electron in time t if it starts from rest.

Now I could get an expression for v by using the first formula, but I don't understand how I can show that v -->c as t --> infinity as t isn't in the equation. I haven't even attempted the second part, but I'm assuming some integration is involved

Can anyone help?

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# The velocity of electron near speed of light?

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