I accelerate a body by a constant force:(adsbygoogle = window.adsbygoogle || []).push({});

[tex]a = F/m = F \frac{\sqrt{1-v^2/c^2}}{m_0} [/tex]

I simplify it by fixingF = m0 = c = 1:

[tex]\frac{dv}{dt} = {\sqrt{1-v^2} [/tex]

This diff equation formalizes the dependence of relativistic body acceleration on its velocity. To get the speed at time t, I solve it rearranging into

[tex] \int{ \frac{dv}{\sqrt{1-v^2}} = t [/tex]

, which is a handbook integral:t = arcsin v, or. This 1) satisfies the equation and, as the Einstein's correction of Newton implies, 2) slows the initially constant acceleration down to zero asv = sin tvapproaches 1 and 3) precludes super-light speeds. However,sinereaches v=1 in finite amount of time while texts tell that we should approach the speed of light asymptotically in t = ∞. Oscillations is not what I expected. Where is the mistake?

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# The trivial constant force acceleration math

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