To comment on other answers about E=mc^2 and KE=1/2 mv^2, these are just different parts of the relativistic energy E=mc^2 cosh(eta) where eta is the velocity

To comment on other answers about E=mc^2 and KE=1/2 mv^2, these are just different parts of the relativistic energy E=mc^2 cosh(eta) where eta is the velocity parameter. https://en.wikipedia.org/wiki/Proper_velocity https://en.wikipedia.org/wiki/Proper_velocity In terms of the coordinate velocity v, E=mc^2 cosh(atanh(v/c))=mc^2 / sqrt(1-(v/c)^2) = mc^2 (1 + 1/2 (v/c)^2 + 3/8 (v/c)^4 + ... So mc^2 is the irreducible energy due to mass and isn't relevant at low speeds because it doesn't change; the first-order approximation of kinetic energy is just 1/2 mv^2 and higher order terms aren't significant at low speeds. http://www.wolframalpha.com/input/?i=cosh(atanh(b) http://www.wolframalpha.com/input/?i=cosh(atanh(b))