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In everyday use and in
kinematics Kinematics is a subfield of physics, developed in classical mechanics, that describes the motion Image:Leaving Yongsan Station.jpg, 300px, Motion involves a change in position In physics, motion is the phenomenon in which an object changes it ...

kinematics
, the speed (commonly referred to as ''v'') of an object is the
magnitude Magnitude may refer to: Mathematics *Euclidean vector, a quantity defined by both its magnitude and its direction *Magnitude (mathematics), the relative size of an object *Norm (mathematics), a term for the size or length of a vector *Order of ...
of the rate of change of its position with time or the magnitude of the change of its position per unit of time; it is thus a
scalar Scalar may refer to: *Scalar (mathematics), an element of a field, which is used to define a vector space, usually the field of real numbers *Scalar (physics), a physical quantity that can be described by a single element of a number field such as ...
quantity. The average speed of an object in an interval of time is the
distance Distance is a numerical measurement ' Measurement is the number, numerical quantification (science), quantification of the variable and attribute (research), attributes of an object or event, which can be used to compare with other objects or eve ...

distance
travelled by the object divided by the
duration Duration may refer to: * The amount of Time#Terminology, time elapsed between two events * Duration (music) – an amount of time or a particular time interval, often cited as one of the fundamental aspects of music * Duration (philosophy) – a th ...
of the interval; the instantaneous speed is the
limit Limit or Limits may refer to: Arts and media * Limit (music), a way to characterize harmony * Limit (song), "Limit" (song), a 2016 single by Luna Sea * Limits (Paenda song), "Limits" (Paenda song), 2019 song that represented Austria in the Eurov ...
of the average speed as the duration of the time interval approaches zero. Speed has the
dimension In physics Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regular s ...
s of distance divided by time. The
SI unit The International System of Units, known by the international abbreviation SI in all languages and sometimes pleonastically as the SI system, is the modern form of the metric system The metric system is a that succeeded the decimal ...
of speed is the
metre per second The metre per second is an SI derived unit SI derived units are units of measurement ' Measurement is the number, numerical quantification (science), quantification of the variable and attribute (research), attributes of an object or event, wh ...
(m/s), but the most common unit of speed in everyday usage is the
kilometre per hour The kilometre per hour (SI symbol: km/h; abbreviations: kph, kmph, km/hr) is a Units of measurement, unit of speed, expressing the number of kilometres travelled in one hour. History Although the metre was formally defined in 1799, the term "kilom ...
(km/h) or, in the US and the UK,
miles per hour Miles per hour (mph, m.p.h., MPH, or mi/h) is a British imperial and United States customary unit United States customary units (U.S. customary units) are a system of measurements commonly used in the United States The United States o ...
(mph). For air and marine travel the
knot A knot is an intentional complication in cordage which may be practical or decorative, or both. Practical knots are classified by function, including hitches, bend Bend or bends may refer to: Materials * Bend, a curvature in a pipe, tube, o ...
is commonly used. The fastest possible speed at which energy or information can travel, according to
special relativity In physics Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, its Motion (physics), motion and behavior through Spacetime, space and time, and the related entities of energy and force ...
, is the
speed of light The speed of light in vacuum A vacuum is a space Space is the boundless three-dimensional Three-dimensional space (also: 3-space or, rarely, tri-dimensional space) is a geometric setting in which three values (called paramet ...
in a vacuum ''c'' = metres per second (approximately or ).
Matter In classical physics Classical physics is a group of physics theories that predate modern, more complete, or more widely applicable theories. If a currently accepted theory is considered to be modern, and its introduction represented a major ...
cannot quite reach the speed of light, as this would require an infinite amount of energy. In relativity physics, the concept of
rapidity In Theory of relativity, relativity, rapidity is commonly used as a measure for relativistic velocity. Mathematically, rapidity can be defined as the hyperbolic angle that differentiates two frames of reference in relative motion, each frame being a ...
replaces the classical idea of speed.


Definition


Historical definition

Italian physicist
Galileo Galilei Galileo di Vincenzo Bonaiuti de' Galilei (; 15 February 1564 – 8 January 1642) was an Italian astronomer An astronomer is a scientist in the field of astronomy who focuses their studies on a specific question or field outside the ...

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.Hewitt (2006), p. 42 In equation form, that is :v = \frac, where v is speed, d is distance, and t 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 speed

Speed at some instant, or assumed constant during a very short period of time, is called ''instantaneous speed''. By looking at a
speedometer A speedometer or speed meter is a gauge Gauge (US: , UK: or ) may refer to: Measurement * Gauge (instrument) A gauge, in science Science (from the Latin word ''scientia'', meaning "knowledge") is a systematic enterprise that Scie ...

speedometer
, one can read the instantaneous speed of a car at any instant. 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 v is defined as the magnitude of the instantaneous
velocity The velocity of an object is the Time derivative, rate of change of its Position (vector), position with respect to a frame of reference, and is a function of time. Velocity is equivalent to a specification of an object's speed and direction ...

velocity
\boldsymbol, that is, the
derivative In mathematics Mathematics (from Greek: ) includes the study of such topics as numbers (arithmetic and number theory), formulas and related structures (algebra), shapes and spaces in which they are contained (geometry), and quantities ...

derivative
of the position \boldsymbol with respect to
time Time is the continued sequence of existence and event (philosophy), events that occurs in an apparently irreversible process, irreversible succession from the past, through the present, into the future. It is a component quantity of various me ...

time
: :v = \left, \boldsymbol v\ = \left, \dot \ = \left, \frac\\,. If s is the length of the path (also known as the distance) travelled until time t, the speed equals the time derivative of s: :v = \frac. In the special case where the velocity is constant (that is, constant speed in a straight line), this can be simplified to v=s/t. The average speed over a finite time interval is the total distance travelled divided by the time duration.


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. If the average speed and the time of travel are known, the distance travelled can be calculated by rearranging the definition to :d = \boldsymbolt\,. 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 In mathematics, the slope or gradient of a line Line, lines, The Line, or LINE may refer to: Arts, entertainment, and media Films * ''Lines'' (film), a 2016 Greek film * ''The Line'' (2017 film) * ''The Line'' (2009 film) * ''The Line'', ...

slope
of a
tangent line In geometry Geometry (from the grc, γεωμετρία; ''wikt:γῆ, geo-'' "earth", ''wikt:μέτρον, -metron'' "measurement") is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space ...

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 velocity

Speed denotes only how fast an object is moving, whereas
velocity The velocity of an object is the Time derivative, rate of change of its Position (vector), position with respect to a frame of reference, and is a function of time. Velocity is equivalent to a specification of an object's speed and direction ...

velocity
describes both how fast and in which direction the object is moving. 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 A circle is a shape A shape or figure is the form of an object or its external boundary, outline, or external surface File:Water droplet lying on a damask.jpg, Water droplet lying on a damask. Surface tension is high enough to preven ...

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 In geometry Geometry (from the grc, γεωμετρία; ' "earth", ' "measurement") is, with , one of the oldest branches of . It is concerned with properties of space that are related with distance, shape, size, and relative position ...
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 Displacement may refer to: Physical sciences Mathematics and Physics *Displacement (geometry), is the difference between the final and initial position of a point trajectory (for instance, the center of mass of a moving object). The actual path c ...
between the starting and end points, whereas the average ''speed'' considers only the total
distance Distance is a numerical measurement ' Measurement is the number, numerical quantification (science), quantification of the variable and attribute (research), attributes of an object or event, which can be used to compare with other objects or eve ...

distance
travelled.


Tangential speed

Linear speed is the distance travelled per unit of time, while tangential speed (or tangential velocity) is the linear speed of something moving along a circular path.Hewitt (2006), p. 131 A point on the outside edge of a
merry-go-round A carousel (American English: from French ''carrousel'' and Italian ''carosello''), roundabout (British English), or merry-go-round, is a type of amusement ride consisting of a rotation, rotating circular platform with seats for riders. The "se ...
or
turntable A phonograph, in its later forms also called a gramophone (as a trademark since 1887, as a generic name in the UK since 1910) or since the 1940s called a record player, is a device for the mechanical recording and reproduction of sound I ...

turntable
travels a greater distance in one complete rotation than a point nearer the center. Travelling a greater distance in the same time means a greater speed, and so linear speed is greater on the outer edge of a rotating object than it is closer to the axis. This speed along a circular path is known as ''tangential speed'' because the direction of motion is
tangent In geometry Geometry (from the grc, γεωμετρία; ' "earth", ' "measurement") is, with , one of the oldest branches of . It is concerned with properties of space that are related with distance, shape, size, and relative position ...
to the
circumference In geometry Geometry (from the grc, γεωμετρία; ' "earth", ' "measurement") is, with , one of the oldest branches of . It is concerned with properties of space that are related with distance, shape, size, and relative position ...
of the circle. For circular motion, the terms linear speed and tangential speed are used interchangeably, and both use units of m/s, km/h, and others.
Rotational speed Rotational speed (also known as speed of revolution or rate of rotation), of an object rotating around an axis is the number of turns of the object divided by time, specified as revolutions per minute Revolutions per minute (abbreviated r ...
(or ''angular speed'') involves the number of revolutions per unit of time. All parts of a rigid merry-go-round or turntable turn about the axis of rotation in the same amount of time. Thus, all parts share the same rate of rotation, or the same number of rotations or revolutions per unit of time. It is common to express rotational rates in revolutions per minute (RPM) or in terms of the number of "radians" turned in a unit of time. There are little more than 6 radians in a full rotation (2 radians exactly). When a direction is assigned to rotational speed, it is known as rotational velocity or
angular velocity In physics, angular velocity (\boldsymbol or \boldsymbol), also known as angular frequency vector,(UP1) is a vector measure of rotation rate, that refers to how fast an object rotates or revolves relative to another point, i.e. how fast the angu ...

angular velocity
. Rotational velocity is a vector whose magnitude is the rotational speed. Tangential speed and rotational speed are related: the greater the RPMs, the larger the speed in metres per second. Tangential speed is directly proportional to rotational speed at any fixed distance from the axis of rotation. However, tangential speed, unlike rotational speed, depends on radial distance (the distance from the axis). For a platform rotating with a fixed rotational speed, the tangential speed in the centre is zero. Towards the edge of the platform the tangential speed increases proportional to the distance from the axis. In equation form: :v \propto \!\, r \omega\,, where ''v'' is tangential speed and ω (Greek letter
omega Omega (; capital Capital most commonly refers to: * Capital letter Letter case (or just case) is the distinction between the letters that are in larger uppercase or capitals (or more formally ''majuscule'') and smaller lowercase (o ...

omega
) is rotational speed. One moves faster if the rate of rotation increases (a larger value for ω), and one also moves faster if movement farther from the axis occurs (a larger value for ''r''). Move twice as far from the rotational axis at the centre and you move twice as fast. Move out three times as far and you have three times as much tangential speed. In any kind of rotating system, tangential speed depends on how far you are from the axis of rotation. When proper units are used for tangential speed ''v'', rotational speed ω, and radial distance ''r'', the direct proportion of ''v'' to both ''r'' and ω becomes the exact equation :v = r\omega\,. Thus, tangential speed will be directly proportional to ''r'' when all parts of a system simultaneously have the same ω, as for a wheel, disk, or rigid wand.


Units

Units of speed include: *
metres per second The metre per second is an SI derived unit SI derived units are units of measurement derived from the seven SI base unit, base units specified by the International System of Units (SI). They are either dimensionless quantity, dimensionless or ...
(symbol m s−1 or m/s), the
SI derived unit SI derived units are units of measurement derived from the seven SI base unit, base units specified by the International System of Units (SI). They are either dimensionless quantity, dimensionless or can be expressed as a product of one or more o ...
; *
kilometres per hour The kilometre per hour (SI symbol: km/h; abbreviations: kph, kmph, km/hr) is a Units of measurement, unit of speed, expressing the number of kilometres travelled in one hour. History Although the metre was formally defined in 1799, the term "kil ...
(symbol km/h); *
miles per hour Miles per hour (mph, m.p.h., MPH, or mi/h) is a British imperial and United States customary unit United States customary units (U.S. customary units) are a system of measurements commonly used in the United States The United States o ...
(symbol mi/h or mph); * knots (
nautical mile A nautical mile is a unit of length A unit of length refers to any arbitrarily chosen and accepted reference standard for measurement of length. The most common units in modern use are the metric system, metric units, used in every country gl ...
s per hour, symbol kn or kt); *
feet per secondThe foot per second (plural feet per second) is a unit Unit may refer to: Arts and entertainment * UNIT, a fictional military organization in the science fiction television series ''Doctor Who'' * Unit of action, a discrete piece of action (or beat) ...
(symbol fps or ft/s); *
Mach number #REDIRECT Mach number#REDIRECT Mach number 300px, An F/A-18 Hornet creating a vapor cone at transonic speed">vapor_cone.html" ;"title="F/A-18 Hornet creating a vapor cone">F/A-18 Hornet creating a vapor cone at transonic speed just before reachi ...
(
dimensionless In dimensional analysis In engineering and science, dimensional analysis is the analysis of the relationships between different physical quantities by identifying their base quantity, base quantities (such as length, mass, time, and electric curre ...
), speed divided by the
speed of sound The speed of sound is the distance travelled per unit of time by a sound wave as it propagates through an elasticity (solid mechanics), elastic medium. At , the speed of sound in air is about , or one kilometre in or one mile in . It depends s ...
; *in
natural units In physics Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, its Motion (physics), motion and behavior through Spacetime, space and time, and the related entities of energy and force. "Phy ...
(dimensionless), speed divided by the
speed of light The speed of light in vacuum A vacuum is a space Space is the boundless three-dimensional Three-dimensional space (also: 3-space or, rarely, tri-dimensional space) is a geometric setting in which three values (called paramet ...
in vacuum (symbol ''c'' = ).


Examples of different speeds


Psychology

According to
Jean Piaget Jean Piaget (, , ; 9 August 1896 – 16 September 1980) was a Swiss Swiss may refer to: * the adjectival form of Switzerland *Swiss people Places *Swiss, Missouri *Swiss, North Carolina *Swiss, West Virginia *Swiss, Wisconsin Other uses *Swiss ...

Jean Piaget
, the intuition for the notion of speed in humans precedes that of duration, and is based on the notion of outdistancing. Piaget studied this subject inspired by a question asked to him in 1928 by
Albert Einstein Albert Einstein ( ; ; 14 March 1879 – 18 April 1955) was a German-born theoretical physicist, widely acknowledged to be one of the greatest physicists of all time. Einstein is known for developing the theory of relativity The theo ...

Albert Einstein
: "In what order do children acquire the concepts of time and speed?" 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."


See also


References

* , Robert B. Leighton, Matthew Sands.
The Feynman Lectures on Physics ''The Feynman Lectures on Physics'' is a physics textbook based on some lectures by Richard Feynman, a Nobel laureate who has sometimes been called "The Great Explainer". The lectures were presented before undergraduate students at the Californ ...

The Feynman Lectures on Physics
, Volume I, Section 8–2.
Addison-Wesley Addison-Wesley is a publisher of textbooks and computer literature. It is an Imprint (trade name), imprint of Pearson PLC, a global publishing and education company. In addition to publishing books, Addison-Wesley also distributes its technical titl ...
, Reading, Massachusetts (1963). . {{Authority control Physical quantities Temporal rates Velocity