View source for Speed

{{Short description|Magnitude of velocity}}
{{About|the property of moving bodies|other uses|Speed (disambiguation)}}
{{pp-semi-indef|small=yes}}
{{more citations needed|date=July 2016}}
{{Use Oxford spelling|date=September 2019}}
{{Infobox physical quantity
| name = Speed
| image = Motorcyclist in Midtown Manhattan-L1002704.jpg
| image_size = 250px
| caption = Speed can be thought of as the rate at which an object covers distance. A fast-moving object has a high speed and covers a relatively large distance in a given amount of time, while a slow-moving object covers a relatively small amount of distance in the same amount of time.
| unit = m/s, m&nbsp;s<sup>−1</sup>
| symbols = ''v''
| dimension = '''L''' '''T'''<sup>−1</sup>
}}
In [[kinematics]], the '''speed''' (commonly referred to as '''''v''''') of an object is the [[magnitude (mathematics)|magnitude]] of the change of its [[Position (vector)|position]] over time or the magnitude of the change of its position per unit of time; it is thus a non-negative [[Scalar (physics)|scalar]] quantity.<ref name="HSM2023">{{cite web|title=Origin of the speed/velocity terminology|publisher=History of Science and Mathematics Stack Exchange |url=https://hsm.stackexchange.com/questions/10984/why-are-speed-and-velocity-not-given-the-same-name/|access-date=12 June 2023}} Introduction of the speed/velocity terminology by Prof. Tait, in 1882.</ref> The '''average speed''' of an object in an interval of time is the [[distance]] travelled by the object divided by the [[Time in physics|duration]] of the interval;<ref name=":0">{{cite web|url=http://physics.info/velocity/|title=Speed & Velocity|last=Elert|first=Glenn|website=The Physics Hypertextbook|access-date=8 June 2017}}</ref> the '''instantaneous speed''' is the [[limit (mathematics)|limit]] of the average speed as the duration of the time interval approaches zero. Speed is the [[Norm (mathematics)|magnitude]] of [[#Difference between speed and velocity|''velocity'']] (a vector), which indicates additionally the direction of motion.

Speed has the [[dimensional analysis|dimension]]s of distance divided by time. The [[International System of Units|SI unit]] of speed is the [[metre per second]] (m/s), but the most common unit of speed in everyday usage is the [[kilometre per hour]] (km/h) or, in the US and the UK, [[miles per hour]] (mph). For air and marine travel, the [[Knot (unit)|knot]] is commonly used.

The fastest possible speed at which energy or information can travel, according to [[special relativity]], is the [[speed of light]] in vacuum ''c'' = {{val|299792458}} metres per second (approximately {{val|1079000000|u=km/h}} or {{val|671000000|u=mph}}). [[Matter]] cannot quite reach the speed of light, as this would require an infinite amount of energy. In relativity physics, the concept of [[rapidity]] replaces the classical idea of speed.

==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>.

===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.

===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}}

==Units==
{{main|Conversion of units#Speed or velocity}}
Units of speed include:
*[[metres per second]] (symbol m&nbsp;s<sup>−1</sup> or m/s), the [[SI derived unit]];
*[[kilometres per hour]] (symbol km/h);
*[[miles per hour]] (symbol mi/h or mph);
*[[knot (unit)|knots]] ([[nautical mile]]s per hour, symbol kn or kt);
*[[Foot per second|feet per second]] (symbol fps or ft/s);
*[[Mach number]] ([[dimensionless]]), speed divided by the [[speed of sound]];
*in [[natural units]] (dimensionless), speed divided by the [[speed of light]] in vacuum (symbol ''c'' = {{val|299792458|u=m/s}}).

{{Speed conversions}}

==Examples of different speeds==
{{Main|Orders of magnitude (speed)}}
{{More citations needed section|date=May 2013}}
{{excessive examples|section|date=May 2014}}
{| class="wikitable"
|-
! Speed !!m/s !!ft/s !!km/h !!mph !!Notes
|-
| Global average [[sea level rise]]  || {{val|0.00000000011}} || {{val|0.00000000036}} || {{val|0.0000000004}} || {{val|0.00000000025}} || 3.5&nbsp;mm/year<ref>{{cite web |last1=NASA's Goddard Space Flight Center |title=Satellite sea level observations |url=https://climate.nasa.gov/vital-signs/sea-level/ |website=Global Climate Change |publisher=NASA |access-date=20 April 2022}}</ref>
|-
| Approximate rate of [[continental drift]] || {{val|0.0000000013}} || {{val|0.0000000042}} || {{val|0.0000000045}} || {{val|0.0000000028}} || 4&nbsp;cm/year. Varies depending on location.
|-
| Speed of a common [[snail]] || 0.001 || 0.003 || 0.004 || 0.002 || 1 millimetre per second
|-
| A brisk [[walk]] || 1.7 || 5.5 || 6.1 || 3.8 || 
|-
| A typical road cyclist || 4.4 || 14.4 || 16 || 10 || Varies widely by person, terrain, bicycle, effort, weather
|-
| A fast martial arts kick || 7.7 || 25.2 || 27.7 || 17.2 || Fastest kick recorded at 130 milliseconds from floor to target at 1 meter distance. Average velocity speed across kick duration<ref name="KickSpeed">{{Cite web |url=http://www.kickspeed.com.au/Improve-measure-kicking-speed.html |title=Improve Kicking Speed for Martial Arts &#124; Get Fast Kicks! |access-date=2013-08-14 |archive-date=2013-11-11 |archive-url=https://web.archive.org/web/20131111004109/http://www.kickspeed.com.au/Improve-measure-kicking-speed.html |url-status=dead }}</ref>
|-
| [[Sprint runner]]s || 12.2 || 40 || 43.92 || 27 || [[Usain Bolt]]'s [[100 metres]] [[List of world records in athletics|world record]].
|-
| Approximate average speed of road race cyclists || 12.5 || 41.0 || 45 || 28 || On flat terrain, will vary
|-
| Typical suburban speed limit in most of the world || 13.8 || 45.3 || 50 || 30 ||
|-
| [[Taipei 101]] observatory elevator || 16.7 || 54.8 || 60.6 || 37.6 || 1010 m/min
|-
| Typical rural speed limit || 24.6 || 80.66 || 88.5 || 56||
|-
| British National Speed Limit (single carriageway) || 26.8 || 88 || 96.56 || 60 ||
|-
| [[Saffir-Simpson Hurricane Scale#Category 1|Category 1]] hurricane  || 33 || 108 || 119 || 74 || Minimum sustained speed over one minute
|-
| Average peak speed of a cheetah || 33.53 || 110 || 120.7|| 75 ||
|-
| Speed limit on a [[Autoroutes of France|French autoroute]] || 36.1 || 118 || 130 || 81 ||
|-
| Highest recorded human-powered speed || 37.02 || 121.5 || 133.2 || 82.8 ||  [[Sam Whittingham]] in a [[recumbent bicycle]]<ref name="sam">{{cite web |url=http://www.wisil.recumbents.com/wisil/whpsc2009/results.htm |title=The Recumbent Bicycle and Human Powered Vehicle Information Center |access-date=2013-10-12 |url-status=dead|archive-url=https://web.archive.org/web/20130811101125/http://www.wisil.recumbents.com/wisil/whpsc2009/results.htm |archive-date=2013-08-11 }}</ref>
|-
| Average speed of Human sneeze || 44.44 || 145.82 || 160 || 99.42 ||
|-
| [[Muzzle velocity]] of a [[paintball marker]] || 90 || 295 || 320 || 200 || 
|-
| Cruising speed of a [[Boeing 747-8]] passenger jet || 255 || 836 || 917 || 570 || [[Mach number|Mach]] 0.85 at {{val|35000|u=ft}} ({{val|10668|u=m}}) altitude
|-
| Speed of a [[.22 long rifle|.22 caliber long rifle]] bullet || 326.14 || 1070 || 1174.09 || 729.55 ||
|-
| The official [[land speed record]] || 341.1 || 1119.1 || 1227.98 || 763 ||
|-
| The [[speed of sound]] in dry air at sea-level pressure and 20&nbsp;°C || 343 || {{val|1125}} || {{val|1235}} || 768 || [[Mach number|Mach]] 1 by definition. 20&nbsp;°C = 293.15&nbsp;[[kelvins]].
|-
| [[Muzzle velocity]] of a [[7.62×39mm]] cartridge || 710 || {{val|2330}} || {{val|2600}} || {{val|1600}} ||The '''7.62×39mm''' round is a rifle [[Cartridge (weaponry)|cartridge]] of [[Soviet Union|Soviet]] origin
|-
| Official [[flight airspeed record]] for jet engined aircraft || 980 || {{val|3215}} || {{val|3530}} || {{val|2194}} || [[Lockheed SR-71 Blackbird]] 
|-
| [[Space Shuttle]] on re-entry || {{val|7800}} || {{val|25600}} || {{val|28000}} || 17,500 ||
|-
| [[Escape velocity]] on Earth || {{val|11200}} || {{val|36700}} || {{val|40000}} || {{val|25000}} || 11.2&nbsp;km·s<sup>−1</sup>
|-
|''[[Voyager 1]]'' relative velocity to the Sun in 2013 || {{val|17000}} || {{val|55800}} || {{val|61200}} || {{val|38000}} || Fastest heliocentric [[Recessional velocity|recession speed]] of any humanmade object.<ref>{{cite web |url=http://www.daviddarling.info/encyclopedia/F/fastest_spacecraft.html |title=Fastest Spacecraft |first=David |last=Darling |access-date=August 19, 2013}}</ref> (11&nbsp;mi/s)
|-
| Average orbital speed of planet [[Earth]] around the Sun || {{val|29783}} || {{val|97713}} || {{val|107218}} || {{val|66623}} ||
|-
| The fastest recorded speed of [[Helios (spacecraft)|the Helios probes]] || 70,220 || 230,381 || 252,792 || 157,078 || Recognized as the fastest speed achieved by a man-made spacecraft, achieved in [[Heliocentric orbit|solar orbit]].
|-
| Orbital speed of the Sun relative to the center of the galaxy || {{val|251000}} || {{val|823000}} || {{val|904000}} || {{val|561000}}
|-
| Speed of the Galaxy relative to the [[CMB]] || {{val|550000}} || {{val|1800000}} || {{val|2000000}} || {{val|1240000}}
|-
| [[Speed of light]] in [[vacuum]] (symbol ''c'') || {{val|299792458}} || {{val|983571056}} || {{val|1079252848}} || {{val|670616629}} || Exactly {{val|299792458|u=m/s}}, by definition of the [[metre]]
|-
! Speed !!m/s !!ft/s !!km/h !!mph !!Notes
|}
<!-- Could add references for all of these - I think they all come from the linked articles.-->
<!-- Removed these two sentences - put back in later? -->
<!-- Objects that move horizontally as well as vertically (such as [[aircraft]]) distinguish [[V speeds|forward speed]] and [[V speeds|climbing speed]]. -->

==Psychology==
According to [[Jean Piaget]], the intuition for the notion of speed in humans precedes that of duration, and is based on the notion of outdistancing.<ref>Jean Piaget, ''Psychology and Epistemology: Towards a Theory of Knowledge'', The Viking Press, pp. 82–83 and pp. 110–112, 1973. [[SBN (code)|SBN]] 670-00362-x</ref> Piaget studied this subject inspired by a question asked to him in 1928 by [[Albert Einstein]]: "In what order do children acquire the concepts of time and speed?"<ref>{{Cite journal|last1=Siegler|first1=Robert S.|last2=Richards|first2=D. Dean|date=1979|title=Development of Time, Speed, and Distance Concepts|url=http://www.psy.cmu.edu/~siegler/1979-Siegler-Richards.pdf|journal=Developmental Psychology|language=en|volume=15|issue=3|pages=288–298|doi=10.1037/0012-1649.15.3.288}}</ref> Children's early concept of speed is based on "overtaking", taking only temporal and spatial orders into consideration, specifically: "A moving object is judged to be more rapid than another when at a given moment the first object is behind and a moment or so later ahead of the other object."<ref>{{cite book|title=Early Years Education: Histories and Traditions, Volume 1|url=https://books.google.com/books?id=VoKOEJTNxGEC&pg=PA164|year=2006|publisher=Taylor & Francis|page=164|isbn = 9780415326704}}</ref>

==See also==
*[[Air speed]]
*[[List of vehicle speed records]]
*[[Projectile#Typical projectile speeds|Typical projectile speeds]]
*[[Speedometer]]
*[[V speeds]]

==References==
{{Wiktionary|speed|swiftness}}
{{wikiquote}}
{{Commons category}}
{{Reflist}}
{{Refbegin}}
* {{cite book | last=Hewitt | first=P.G. | title=Conceptual Physics | publisher=Pearson Education | year=2007 | isbn=978-81-317-1553-6 | url=https://books.google.com/books?id=A5HylF_5tLEC | access-date=2023-07-20}}
* [[Richard Feynman|Richard P. Feynman]], Robert B. Leighton, Matthew Sands. [[The Feynman Lectures on Physics]], Volume I, [https://feynmanlectures.caltech.edu/I_08.html#Ch8-S2 Section 8–2]. [[Addison-Wesley]], Reading, Massachusetts (1963). {{ISBN|0-201-02116-1}}.
{{Refend}}

{{Kinematics}}
{{Classical mechanics derived SI units}}
{{Authority control}}

[[Category:Velocity|*]]
[[Category:Physical quantities]]
[[Category:Temporal rates]]