Editing Speed (section)

==Definition==
=== Historical definition ===
Italian physicist [[Galileo Galilei]] is usually credited with being the first to measure speed by considering the distance covered and the time it takes. Galileo defined speed as the distance covered per unit of time.<ref name="Hewitt 2007, p. 42">{{harvnb|Hewitt|2007|p=42}}</ref> In equation form, that is
<math display=block qid=Q3711325 id=main_formula>v = \frac{d}{t},</math>
where <math>v</math> is speed, <math>d</math> is distance, and <math>t</math> is time. A cyclist who covers 30 metres in a time of 2 seconds, for example, has a speed of 15 metres per second. Objects in motion often have variations in speed (a car might travel along a street at 50&nbsp;km/h, slow to 0&nbsp;km/h, and then reach 30&nbsp;km/h).

===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.

===Average speed===
[[File:20230703 Average speed of bowling ball versus travel time.svg |thumb |As an example, a bowling ball's speed when first released will be above its average speed, and after decelerating because of friction, its speed when reaching the pins will be below its average speed.]]
Different from instantaneous speed, ''average speed'' is defined as the total distance covered divided by the time interval. For example, if a distance of 80 kilometres is driven in 1 hour, the average speed is 80 kilometres per hour. Likewise, if 320 kilometres are travelled in 4 hours, the average speed is also 80 kilometres per hour. When a distance in kilometres (km) is divided by a time in hours (h), the result is in kilometres per hour (km/h).

Average speed does not describe the speed variations that may have taken place during shorter time intervals (as it is the entire distance covered divided by the total time of travel), and so average speed is often quite different from a value of instantaneous speed.<ref name="Hewitt 2007, p. 42" /> If the average speed and the time of travel are known, the distance travelled can be calculated by rearranging the definition to
<math display="block">d = \boldsymbol{\bar{v}}t\,.</math>

Using this equation for an average speed of 80 kilometres per hour on a 4-hour trip, the distance covered is found to be 320 kilometres.

Expressed in graphical language, the [[slope]] of a [[tangent line]] at any point of a distance-time graph is the instantaneous speed at this point, while the slope of a [[chord (geometry)|chord line]] of the same graph is the average speed during the time interval covered by the chord. Average speed of an object is
Vav = s÷t

===Difference between speed and velocity===
Speed denotes only how fast an object is moving, whereas [[velocity]] describes both how fast and in which direction the object is moving.<ref>{{cite book| last=Wilson | first=Edwin Bidwell | title=Vector analysis: a text-book for the use of students of mathematics and physics, founded upon the lectures of J. Willard Gibbs | series=Yale bicentennial publications | year=1901 | pages=125 | publisher=C. Scribner's Sons | hdl=2027/mdp.39015000962285?urlappend=%3Bseq=149}} This is the likely origin of the speed/velocity terminology in vector physics.</ref> If a car is said to travel at 60&nbsp;km/h, its ''speed'' has been specified. However, if the car is said to move at 60&nbsp;km/h to the north, its ''velocity'' has now been specified.

The big difference can be discerned when considering movement around a [[circle]]. When something moves in a circular path and returns to its starting point, its average ''velocity'' is zero, but its average ''speed'' is found by dividing the [[circumference]] of the circle by the time taken to move around the circle. This is because the average ''velocity'' is calculated by considering only the [[Displacement (vector)|displacement]] between the starting and end points, whereas the average ''speed'' considers only the total [[distance]] travelled.

===Tangential speed===
{{excerpt|Tangential speed|templates=-Classical mechanics}}