![]() Things formally for a different point of view, possibly new to a physicist ![]() But I think it might be useful to restate the tiny increment of distance traveled - is the same as the magnitude of the differential of displacement ($d\mathbf|$? ![]() It's just that in the case of instantaneous speed, the absolute value of velocity happens to be equal to the speed because the magnitude of the differential of arc length ($ds$) - i.e. ![]() The actual definition of speed in both cases really is distance traveled over the time taken to travel it. There error is the magnitude of velocity is not actually a definition, but is better appreciated as a consequence of the actual definition, and any materials that say it is are problematic study materials.
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