= Solution
The relativistic energy of a particle of <rest mass> $m$ is $E=\gamma mc^2$, where the <Lorentz factor> is $\gamma=(1-v^2/c^2)^{-1/2}$. Using the <binomial series> at small $v/c$ gives
$$
\boxed{E=mc^2+\frac12mv^2+O\left(\frac{mv^4}{c^2}\right).}
$$
The second term is the familiar Newtonian <kinetic energy>. The first is the <rest energy>, which remains when $v=0$. Thus the new physical idea is \b[mass-energy equivalence: a body's mass represents energy $mc^2$ even at rest]. The total energy is not merely energy due to motion.
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