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Where does the relativistic formula

$$p~=~\frac{1}{c}\sqrt{T^2 +2mTc^2}$$

come from? What is the derivation from Einstein's formula? $T$ is the kinetic energy $m$ is the mass $p$ is the momentum.

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    $\begingroup$ Can you add a bit more context? what is $T$ here? $\endgroup$ – By Symmetry Jul 26 '15 at 12:40
  • $\begingroup$ Some more context on where you saw this equation would be better as well. $\endgroup$ – Kyle Kanos Jul 26 '15 at 14:45
  • $\begingroup$ In /gamma decay $\endgroup$ – physnolimits Jul 26 '15 at 14:46
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We can write total energy $E$ two ways: \begin{equation} E^2=p^2c^2+m^2c^4 \\ E=T+mc^2, \end{equation} where $T$ is kinetic energy. Eliminating $E$ from those two equations will give you the desired result.

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Hint: $T = E - E_0 = m\gamma c^2 - mc^2 = mc^2(\gamma -1)$ and $p = |\vec p| = m\gamma |\vec v| = m\gamma v$

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