Editing Speed (section)

===Instantaneous speed===
Speed at some instant, or assumed constant during a [[infinitesimal|very short]] period of time, is called ''instantaneous speed''. By looking at a [[speedometer]], one can read the instantaneous speed of a car at any instant.<ref name="Hewitt 2007, p. 42"/> A car travelling at 50&nbsp;km/h generally goes for less than one hour at a constant speed, but if it did go at that speed for a full hour, it would travel 50&nbsp;km. If the vehicle continued at that speed for half an hour, it would cover half that distance (25&nbsp;km). If it continued for only one minute, it would cover about 833&nbsp;m.

In mathematical terms, the instantaneous speed <math>v</math> is defined as the magnitude of the instantaneous [[velocity]] <math>\boldsymbol{v}</math>, that is, the [[derivative]] of the position <math>\boldsymbol{r}</math> with respect to [[time]]:<ref name=":0" /><ref>{{Cite web | url=http://www.electropedia.org/iev/iev.nsf/display?openform&ievref=113-01-33|title=IEC 60050 - Details for IEV number 113-01-33: "speed" | website=Electropedia: The World's Online Electrotechnical Vocabulary|access-date=2017-06-08}}</ref>
<math display="block">v = \left|\boldsymbol v\right| = \left|\dot {\boldsymbol r}\right| = \left|\frac{d\boldsymbol r}{dt}\right|\,.</math>

If <math>s</math> is the length of the path (also known as the distance) travelled until time <math>t</math>, the speed equals the time derivative of <math>s</math>:<ref name=":0" />
<math display="block">v = \frac{ds}{dt}.</math>

In the special case where the velocity is constant (that is, constant speed in a straight line), this can be simplified to <math>v = s/t</math>.  The average speed over a finite time interval is the total distance travelled divided by the time duration.