The jerk setting in 3D printing gcode and firmware represents a concept similar to, but distinct from, the physical definition of jerk. Rather, it's a [limit on] instantaneous change of speed.

Mathematically, one way to make sense of this is to think that, rather than being the second derivative of speed with respect to time, this "jerk" is the entire remainder of the first-order expansion of speed with respect to time - it corresponds to the second-order term and all higher order terms. Such terms cannot be combined just as coefficients, since they all have different units corresponding to different powers of time; rather, they can be combined only with their corresponding powers of time, in which case the resulting unit is mm/s.

The jerk setting in 3D printing G-code and firmware represents a concept similar to, but distinct from, the physical definition of jerk. Rather, it's a [limit on] instantaneous change of speed.

Mathematically, one way to make sense of this is to think that, rather than being the second derivative of speed with respect to time, this "jerk" is the entire remainder of the first-order expansion of speed with respect to time - it corresponds to the second-order term and all higher order terms. Such terms cannot be combined just as coefficients, since they all have different units corresponding to different powers of time; rather, they can be combined only with their corresponding powers of time, in which case the resulting unit is mm/s.