- #1

psal

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## Homework Statement

I proved that a relativistic 1D force is

F = [itex]\gamma[/itex]

^{3}*m*dVx/dt = m * dVx/dt * 1/ (1 - (v/c)

^{2})

^{3/2}

Then, "This is a separable differential equation that can be solved using a trig

substitution. Use this (or some other technique that works) to show that the velocity is given by

v(t) = [itex]\frac{a*t}{\sqrt{1 + \frac{at}{c}

^{2}}}[/itex]

## Homework Equations

a = [itex]\frac{dVx}{dt}[/itex] * [itex]\frac{1}{(1-\frac{v}{c}

^{3/2}}[/itex]

β = [itex]\frac{v}{c}[/itex] = sinΘ

cosΘ = [itex]\sqrt{1 - β

^{2}}[/itex]

## The Attempt at a Solution

dβ = cosθdθ

a(t) = [itex]\frac{c*cosθdθ}{cos

^{2}θ}[/itex] = [itex]\frac{cdθ}{cosθ}[/itex]

I don't really know what to do from here to arive at the answer

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