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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 - β2}[/itex]
The Attempt at a Solution
dβ = cosθdθ
a(t) = [itex]\frac{c*cosθdθ}{cos2θ}[/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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