Specific kinetic energy ($K/m=|\mathbf{v}{|}^2/2$)

Kinetic energy per unit mass. For an acceleration field $\mathbf{a}$, its change along an actual trajectory is $\Delta (|\mathbf{v}{|}^2/2)=\int \mathbf{a}\cdot d\mathbf{r}$, by the chain rule. This differs by a mass factor from the work integral of a physical force.