I've been reading through a book on relativity and I came across this(adsbygoogle = window.adsbygoogle || []).push({});

[itex]\mathcal{E}=p . v - L[/itex]

[itex]\mathcal{E} =\frac{m v}{\sqrt{1-\frac{v^2}{c^2}}}.v + m c^2\sqrt{1-\frac{v^2}{c^2}}[/itex]

I know this part well enough but then the book arrives at

[itex]\mathcal{E}=\frac{m c^2}{\sqrt{1-\frac{v^2}{c^2}}}[/itex]

How did that happen?

All I can get is this

[itex]\mathcal{E} =\frac{m v^2}{\sqrt{1-\frac{v^2}{c^2}}} + m c^2\sqrt{1-\frac{v^2}{c^2}}\neq \frac{m c^2}{\sqrt{1-\frac{v^2}{c^2}}}[/itex]

What am I doing wrong here?

Thanks in advance

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# Just a quick question on the derivation of energy

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