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I was reading a book and came across a formula which gives relativistic kinetic energy of a moving body with velocity $v=ßc$, where $c$ is speed of light. The formula is shown in image (equation number 1.12)

Relativisttic Energy

What I need to know is how for small values of ß, equation 1.12 becomes equation 1.13?

Qmechanic
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Manu Nair
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1 Answers1

3

Taylor series to first order:

$$ \frac 1 {1-\epsilon} \approx 1 + \epsilon $$ $$ \sqrt{1 + \epsilon} \approx 1 + \frac 1 2 \epsilon $$

JEB
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