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Shown relativistic KE reduces to classical KE in low speed limit
:<math>m_0</math> is the [[rest mass]]
:<math>m_0</math> is the [[rest mass]]
:<math>c</math> is the [[speed of light]]
:<math>c</math> is the [[speed of light]]
This can be shown to be equivalent to the classical equation for kinetic energy, <math>K=\frac{1}{2} m_0 v^2</math>, by performing a binomial expansion on it. Using the result:
<math>
(1+x)^n = 1 + nx+ \frac{n(n-1)x^2}{2} + ...
</math>
Expanding the [[Lorentz factor]] in this way, we see:
<math>
K=(1 + \frac{1}{2} \frac{v^2}{c^2}+ \frac{3}{8} \frac{v^4}{c^4}+...-1) m_0 c^2
</math>
This simplifies to
<math>
K=\frac{1}{2} m_0 v^2 + \frac{3}{8} \frac{m_0 v^4}{c^2} +...
</math>
For speeds encountered everyday, which are a lot less than that of [[speed of light|light] (such that <math>v<<c</math>), all terms apart from the first are very small and can be neglected. Hence, the formula reduces to:
<math>K \approx \frac{1}{2} m_0 v^2</math>
which is the classical formula.
===Derivation===
===Derivation===
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