CoachThe instantaneous speed of a motion at some moment is the average speed over a very short interval around that moment — so short that the motion has no room to change its pace within it. It is the speedometer’s number and the radar’s: both, in fact, measure exactly as Method 65.2 does, over ticks of a wink. (What “very short” means with full rigor is the great question the last year of high school mathematics answers — and the answer created modern science.)
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Example 65.6 (Average and instantaneous, side by side)
A metro run between stations: average speed — total distance over total time — . Instantaneous speed: at both platforms, mid-tunnel. In uniform motion, and only there, the two notions merge into one steady number: uniform motion is precisely the motion that makes speed a single, honest, interval-free quantity.