Speed

Template:Short description Template:About Template:Pp-semi-indef Template:More citations needed Template:Use Oxford spelling Template:Infobox physical quantity In kinematics, the speed (commonly referred to as v) of an object is the magnitude of the change of its position over time or the magnitude of the change of its position per unit of time; it is thus a non-negative scalar quantity.<ref name="HSM2023">{{#invoke:citation/CS1|citation |CitationClass=web }} 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 duration of the interval;<ref name=":0">{{#invoke:citation/CS1|citation |CitationClass=web }}</ref> the instantaneous speed is the limit of the average speed as the duration of the time interval approaches zero. Speed is the magnitude of velocity (a vector), which indicates additionally the direction of motion.

Speed has the dimensions of distance divided by time. The 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 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 = Template:Val metres per second (approximately Template:Val or Template:Val). 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.

DefinitionEdit

Historical definitionEdit

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">Template:Harvnb</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 km/h, slow to 0 km/h, and then reach 30 km/h).

Instantaneous speedEdit

Speed at some instant, or assumed constant during a 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 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 km. If the vehicle continued at that speed for half an hour, it would cover half that distance (25 km). If it continued for only one minute, it would cover about 833 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>{{#invoke:citation/CS1|citation |CitationClass=web }}</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 speedEdit

File:20230703 Average speed of bowling ball versus travel time.svg

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 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 velocityEdit

Speed denotes only how fast an object is moving, whereas velocity describes both how fast and in which direction the object is moving.<ref>Template:Cite book This is the likely origin of the speed/velocity terminology in vector physics.</ref> If a car is said to travel at 60 km/h, its speed has been specified. However, if the car is said to move at 60 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 between the starting and end points, whereas the average speed considers only the total distance travelled.

Tangential speedEdit

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UnitsEdit

{{#invoke:Labelled list hatnote|labelledList|Main article|Main articles|Main page|Main pages}} Units of speed include:

metres per second (symbol m s⁻¹ or m/s), the SI derived unit;
kilometres per hour (symbol km/h);
miles per hour (symbol mi/h or mph);
knots (nautical miles per hour, symbol kn or kt);
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 = Template:Val).

Template:Speed conversions

Examples of different speedsEdit

Template:More citations needed section Template:Excessive examples {{#invoke:Labelled list hatnote|labelledList|Main article|Main articles|Main page|Main pages}}

Speed	m/s	ft/s	km/h	mph	Notes
Global average sea level rise	Template:Val	Template:Val	Template:Val	Template:Val	citation	CitationClass=web }}</ref>
Approximate rate of continental drift	Template:Val	Template:Val	Template:Val	Template:Val	4 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	citation	CitationClass=web }}</ref>
Sprint runners	12.2	40	43.92	27	Usain Bolt's 100 metres 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
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 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">{{#invoke:citation/CS1\|citation	CitationClass=web }}</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 0.85 at Template:Val (Template:Val) altitude
Speed of a .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 °C	343	Template:Val	Template:Val	768	Mach 1 by definition. 20 °C = 293.15 kelvins.
Muzzle velocity of a 7.62×39mm cartridge	710	Template:Val	Template:Val	Template:Val	The 7.62×39mm round is a rifle cartridge of Soviet origin
Official flight airspeed record for jet engined aircraft	980	Template:Val	Template:Val	Template:Val	Lockheed SR-71 Blackbird
Space Shuttle on re-entry	Template:Val	Template:Val	Template:Val	17,500
Escape velocity on Earth	Template:Val	Template:Val	Template:Val	Template:Val	11.2 km·s⁻¹
Voyager 1 relative velocity to the Sun in 2013	Template:Val	Template:Val	Template:Val	Template:Val	Fastest heliocentric recession speed of any humanmade object.<ref>{{#invoke:citation/CS1\|citation	CitationClass=web }}</ref> (11 mi/s)
Average orbital speed of planet Earth around the Sun	Template:Val	Template:Val	Template:Val	Template:Val
The fastest recorded speed of the Helios probes	70,220	230,381	252,792	157,078	Recognized as the fastest speed achieved by a man-made spacecraft, achieved in solar orbit.
Orbital speed of the Sun relative to the center of the galaxy	Template:Val	Template:Val	Template:Val	Template:Val
Speed of the Galaxy relative to the CMB	Template:Val	Template:Val	Template:Val	Template:Val
Speed of light in vacuum (symbol c)	Template:Val	Template:Val	Template:Val	Template:Val	Exactly Template:Val, by definition of the metre
Speed	m/s	ft/s	km/h	mph	Notes

PsychologyEdit

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 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>Template:Cite journal</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>Template:Cite book</ref>