Energy is the capacity to do work, and mechanics keeps it in two everyday accounts. Both are measured in joules, both can be paid into and drawn out of, and the whole subject is bookkeeping between them.

The motion account is kinetic energy: $E_k = \tfrac{1}{2} m v^{2}$, read aloud E-k equals one-half m v squared, with $E_k$ the kinetic energy in joules, $m$ the mass in kilograms and $v$ the speed in metres per second. Two features do all the damage. The square: double the speed and you QUADRUPLE the energy, which is why a crash at 60 is four times the event a crash at 30 is, and why every stopping distance chart curves. And the half: it is not decoration — it is the average of a speed that grew from nothing, and dropping it doubles every answer you will ever write.

The height account is gravitational potential energy: $U = mgh$, read aloud U equals m g h, with $U$ in joules, $m$ the mass in kilograms, $g$ the 9.81 m/s² the planet charges, and $h$ the height RISEN, in metres, measured from whatever level you declare to be zero. That last part is not a loophole; it is the honest truth about potential energy. Only CHANGES in height matter, so pick the floor, the bench or the sea and say so.

One nugget to keep the units honest: $\mathrm{kg \cdot m^2/s^2}$ is a joule, and both relations land there. $mgh$ is kg × m/s² × m — a newton times a metre. $\tfrac{1}{2}mv^2$ is kg × m²/s². Same unit, two accounts, one currency.