No motion as zero speed or pace

What does “no motion” mean for the measurement of speed or pace? There are two cases of no motion: either (1) the trajectory length is zero or (2) the trajectory duration is zero.

Consider first the speed ratio (Δr/Δt).

(1) the trajectory length is zero: then the speed is zero because it equals zero length divided by the nonzero duration of the independent motion.

(2) the trajectory duration is zero: this possibility is excluded by the independence of the duration.

Consider the pace ratio (Δt/Δr).

(3) the trajectory length is zero: this possibility is excluded by the independence of the length.

(4) the trajectory duration is zero: then the pace is zero because it equals zero duration divided by the nonzero lengthof the independent motion.

Case (4) seems strange but consider a stopwatch that is clicked on, and then immediately clicked off. There would be no motion in that instant. But the length interval for the pace is independent of this and the unit of length is nonzero. So the pace would be a zero duration divided by a nonzero length, which equals zero.