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

Consider first the speed ratio (Δr/Δt).

(1) the trajectory distance is zero: then the speed is zero because it equals zero distance 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 distance is zero: this possibility is excluded by the independence of the distance.

(4) the trajectory duration is zero: then the pace is zero because it equals zero duration divided by the nonzero distance of 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 distance interval for the pace is independent of this and the unit of distance is nonzero. So the pace would be a zero duration divided by a nonzero distance, which equals zero.

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