In
kinematicsKinematics is the branch of classical mechanics that describes the motion of bodies and systems without consideration of the forces that cause the motion....
, the
speed of an object is the
magnitudeThe magnitude of an object in mathematics is its size: a property by which it can be compared as larger or smaller than other objects of the same kind; in technical terms, an ordering of the class of objects to which it belongs....
of its
velocityIn physics, velocity is speed in a given direction. Speed describes only how fast an object is moving, whereas velocity gives both the speed and direction of the object's motion. To have a constant velocity, an object must have a constant speed and motion in a constant direction. Constant ...
(the
rate of changeA time derivative is a derivative of a function with respect to time, usually interpreted as the rate of change of the value of the function. The variable denoting time is usually written as t\,.Notation:...
of its position); it is thus a
scalarIn physics, a scalar is a simple physical quantity that is not changed by coordinate system rotations or translations , or by Lorentz transformations or spacetime translations . This is in contrast to a vector...
quantity. The
average speed of an object in an interval of time is the
distanceDistance is a numerical description of how far apart objects are. In physics or everyday discussion, distance may refer to a physical length, or an estimation based on other criteria . In mathematics, a distance function or metric is a generalization of the concept of physical distance...
traveled by the object divided by the
durationTime is a part of the measuring system used to sequence events, to compare the durations of events and the intervals between them, and to quantify rates of change such as the motions of objects....
of the interval; the instantaneous speed is the
limitIn mathematics, the concept of a "limit" is used to describe the value that a function or sequence "approaches" as the input or index approaches some value. The concept of limit allows mathematicians to define a new point from a Cauchy sequence of previously defined points within a complete metric...
of the average speed as the duration of the time interval approaches zero .
Like velocity, speed has the
dimensionIn physics and all science, dimensional analysis is a tool to find or check relations among physical quantities by using their dimensions. The dimension of a physical quantity is the combination of the basic physical dimensions which describe it; for example, speed has the dimension length per...
s of a
lengthIn geometric measurements, length most commonly refers to the longest dimension of an object.In certain contexts, the term "length" is reserved for a certain dimension of an object along which the length is measured. For example it is possible to cut a length of a wire which is shorter than wire...
divided by a
timeTime is a part of the measuring system used to sequence events, to compare the durations of events and the intervals between them, and to quantify rates of change such as the motions of objects....
; the
SI unitThe International System of Units is the modern form of the metric system and is generally a system of units of measurement devised around seven base units and the convenience of the number ten. The older metric system included several groups of units...
of speed is the meter per second, but the most usual unit of speed in everyday usage is the kilometer per hour or, in the USA and the UK,
miles per hourMiles per hour is an imperial unit of speed expressing the number of statute miles covered in one hour. It is currently the standard unit used for speed limits, and to express speeds generally, on roads in the United Kingdom and the United States. It is also often used to express the speed of...
. For air and marine travel the knot is commonly used.
The fastest possible speed at which energy or information can travel, according to
special relativitySpecial relativity is the physical theory of measurement in an inertial frame of reference proposed in 1905 by Albert Einstein in the paper "On the Electrodynamics of Moving Bodies".It generalizes Galileo's...
, is the
speed of lightThe speed of light in vacuum, usually denoted by c, is a physical constant important in many areas of physics. Its value is 299,792,458 metres per second, a figure that is exact since the length of the metre is defined from this constant and the international standard for time...
in vacuum
c = 299,792,458 meters per second, approximately 1079 million kilometers per hour (671,000,000 mph).
MatterMatter is a general term for the substance of which all physical objects consist. Typically, matter includes atoms and other particles which have mass. A common way of defining matter is as anything that has mass and occupies volume...
cannot quite reach the speed of light, as this would require an infinite amount of energy.
Definition
The speed
v is defined as the magnitude of the
velocityIn physics, velocity is speed in a given direction. Speed describes only how fast an object is moving, whereas velocity gives both the speed and direction of the object's motion. To have a constant velocity, an object must have a constant speed and motion in a constant direction. Constant ...
v, that is the
derivativeIn calculus, a branch of mathematics, the derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much one quantity is changing in response to changes in some other quantity; for example, the derivative of the position of a...
of the position
r with respect to
timeTime is a part of the measuring system used to sequence events, to compare the durations of events and the intervals between them, and to quantify rates of change such as the motions of objects....
:
If
s is the length of the path traveled until time
t, the speed equals the time derivative of
s:
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 traveled divided by the time duration.
Expressed in graphical language, the
slopeIn mathematics, the slope or gradient of a line describes its steepness, incline, or grade. A higher slope value indicates a steeper incline....
of a tangent line of a distancetime graph is the instantaneous speed, and the slope of a
chordA chord of a circle is a geometric line segment whose endpoints both lie on the circumference of the circle.A secant or a secant line is the line extension of a chord. More generally, a chord is a line segment joining two points on any curve, such as but not limited to an ellipse...
line of distancetime graph is the average speed over the time interval between the ends of the chord.
Units
Units of speed include:
 meters per second (symbol m s^{−1} or m/s), the SI derived unit
The International System of Units specifies a set of seven base units from which all other units of measurement are formed, by products of the powers of base units. These other units are called SI derived units, for example, the SI derived unit of area is square metre , and of density is...
;
 kilometers per hour (symbol km/h);
 miles per hour
Miles per hour is an imperial unit of speed expressing the number of statute miles covered in one hour. It is currently the standard unit used for speed limits, and to express speeds generally, on roads in the United Kingdom and the United States. It is also often used to express the speed of...
(symbol mph);
 knots (nautical mile
The nautical mile is a unit of length that is about one minute of arc of latitude along any meridian, but is approximately one minute of arc of longitude only at the equator...
s per hour, symbol kn or kt);
 feet per second (symbol fps or ft/s);
 Mach number
Mach number is the speed of an object moving through air, or any other fluid substance, divided by the speed of sound as it is in that substance for its particular physical conditions, including those of temperature and pressure...
(dimensionless), speed divided by the speed of soundThe speed of sound is the distance travelled during a unit of time by a sound wave propagating through an elastic medium. In dry air at , the speed of sound is . This is , or about one kilometer in three seconds or approximately one mile in five seconds....
;
 in natural units
In physics, natural units are physical units of measurement based only on universal physical constants. For example the elementary charge e is a natural unit of electric charge, or the speed of light c is a natural unit of speed...
(dimensionless), speed divided by the speed of lightThe speed of light in vacuum, usually denoted by c, is a physical constant important in many areas of physics. Its value is 299,792,458 metres per second, a figure that is exact since the length of the metre is defined from this constant and the international standard for time...
in vacuum (symbol c = 299,792,458 m/s).
Examples of different speeds
Speed  m/s  ft/s  km/h  mph  Notes 
Approximate rate of continental driftContinental drift is the movement of the Earth's continents relative to each other. The hypothesis that continents 'drift' was first put forward by Abraham Ortelius in 1596 and was fully developed by Alfred Wegener in 1912... 
0.00000001 
0.00000003 
0.00000004 
0.00000002 
4 cm/year. Varies depending on location 
Speed of a common snail Snail is a common name applied to most of the members of the molluscan class Gastropoda that have coiled shells in the adult stage. When the word is used in its most general sense, it includes sea snails, land snails and freshwater snails. The word snail without any qualifier is however more often... 
0.001 
0.003 
0.004 
0.002 
1 millimeter per second. 
A brisk walk WALK may refer to:*WALK , a radio station licensed to East Patchogue, New York, United States*WALKFM, a radio station licensed to Patchogue, New York, United States... 
1.7 
5.5 
6.1 
3.8 
(5.5 feet per second) 
A typical road cyclist 
4.4 
14.4 
16 
10 
Varies wildly by person, terrain, bicycle, effort, weather. 
Sprint runners 
10 
32.8 
36 
22 
Average speed over 100 meters. 
Approximate average speed of road 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 101Taipei 101 , formerly known as the Taipei World Financial Center, is a landmark skyscraper located in Xinyi District, Taipei, Taiwan. The building ranked officially as the world's tallest from 2004 until the opening of the Burj Khalifa in Dubai in 2010... observatory elevator 
16.7 
54.8 
60.6 
37.6 
1010 m/min. 
Typical rural speed limit 
24.6 
80.66 
88.5 
55 

British National Speed Limit (single carriageway) 
26.8 
88 
96.56 
60 

Category 1 hurricane 
33 
108 
119 
74 
Minimum sustained speed over 1 minute 
Speed limit on a French autoroute The Autoroute system in France consists largely of toll roads, except around large cities and in parts of the north. It is a network of worth of motorways. Autoroute destinations are shown in blue, while destinations reached through a combination of autoroutes are shown with an added autoroute logo... 
36.1 
118 
130 
81 

Highest recorded humanpowered speed 
37.02 
121.5 
133.2 
82.8 
Sam WhittinghamSam Whittingham is a Canadian cyclist who has held several world records on recumbent bicycles., he holds the following world records under the sanction of the International Human Powered Vehicle Association:... in a recumbent bicycleA recumbent bicycle is a bicycle that places the rider in a laidback reclining position. Most recumbent riders choose this type of design for ergonomic reasons; the rider's weight is distributed comfortably over a larger area, supported by back and buttocks...

Muzzle velocity Muzzle velocity is the speed a projectile has at the moment it leaves the muzzle of the gun. Muzzle velocities range from approximately to in black powder muskets , to more than in modern rifles with highperformance cartridges such as the .220 Swift and .204 Ruger, all the way to for tank guns... of a paintball markerA paintball marker, also known as a paintball gun, is the main piece of equipment in the sport of paintball. Markers use an expanding gas, such as carbon dioxide or compressed air, to propel paintballs through the barrel. Some paintball players refer to the piece of equipment as a "marker" rather... 
90 
295 
320 
200 

Cruising speed of a Boeing 7478The Boeing 7478 is a widebody jet airliner developed by Boeing Commercial Airplanes. Officially announced in 2005, the 7478 is the fourthgeneration Boeing 747 version, with lengthened fuselage, redesigned wings and improved efficiency... passenger jet 
255 
836 
917 
570 
MachMach number is the speed of an object moving through air, or any other fluid substance, divided by the speed of sound as it is in that substance for its particular physical conditions, including those of temperature and pressure... 0.85 at 35,000 ft altitude 
The official land speed recordThe land speed record is the highest speed achieved by a wheeled vehicle on land. There is no single body for validation and regulation; in practice the Category C flying start regulations are used, officiated by regional or national organizations under the auspices of the Fédération... 
341.1 
1119.1 
1227.98 
763 

The speed of soundThe speed of sound is the distance travelled during a unit of time by a sound wave propagating through an elastic medium. In dry air at , the speed of sound is . This is , or about one kilometer in three seconds or approximately one mile in five seconds.... in dry air at sealevel pressure and 20 °C 
343 
1125 
1235 
768 
MachMach number is the speed of an object moving through air, or any other fluid substance, divided by the speed of sound as it is in that substance for its particular physical conditions, including those of temperature and pressure... 1 by definition. 20 °C = 293 kelvinThe kelvin is a unit of measurement for temperature. It is one of the seven base units in the International System of Units and is assigned the unit symbol K. The Kelvin scale is an absolute, thermodynamic temperature scale using as its null point absolute zero, the temperature at which all... . 
Muzzle velocity Muzzle velocity is the speed a projectile has at the moment it leaves the muzzle of the gun. Muzzle velocities range from approximately to in black powder muskets , to more than in modern rifles with highperformance cartridges such as the .220 Swift and .204 Ruger, all the way to for tank guns... of an AK47 assault rifleAn assault rifle is a selective fire rifle that uses an intermediate cartridge and a detachable magazine. Assault rifles are the standard infantry weapons in most modern armies... bulletA bullet is a projectile propelled by a firearm, sling, or air gun. Bullets do not normally contain explosives, but damage the intended target by impact and penetration... 
710 
2,330 
2,600 
1600 

Official flight airspeed record 
980 
3,215 
3,530 
2,194 

Space shuttleThe Space Shuttle was a manned orbital rocket and spacecraft system operated by NASA on 135 missions from 1981 to 2011. The system combined rocket launch, orbital spacecraft, and reentry spaceplane with modular addons... on reentry 
7,800 
25,600 
28,000 
17,500 

Escape velocityIn physics, escape velocity is the speed at which the kinetic energy plus the gravitational potential energy of an object is zero gravitational potential energy is negative since gravity is an attractive force and the potential is defined to be zero at infinity... on Earth 
11,200 
36,700 
40,000 
25,000 
11.2 km∙s^{−1} 
Average orbital speed of planet EarthEarth is the third planet from the Sun, and the densest and fifthlargest of the eight planets in the Solar System. It is also the largest of the Solar System's four terrestrial planets... 
29,783 
97,713 
107,218 
66,623 

Speed of lightThe speed of light in vacuum, usually denoted by c, is a physical constant important in many areas of physics. Its value is 299,792,458 metres per second, a figure that is exact since the length of the metre is defined from this constant and the international standard for time... in vacuumIn everyday usage, vacuum is a volume of space that is essentially empty of matter, such that its gaseous pressure is much less than atmospheric pressure. The word comes from the Latin term for "empty". A perfect vacuum would be one with no particles in it at all, which is impossible to achieve in... (symbol c) 
299,792,458 
983,571,056 
1,079,252,848 
670,616,629 
Exactly 299,792,458 m∙s^{−1}, by definition of the meterThe metre , symbol m, is the base unit of length in the International System of Units . Originally intended to be one tenmillionth of the distance from the Earth's equator to the North Pole , its definition has been periodically refined to reflect growing knowledge of metrology... . 
Vehicles often have a
speedometerA speedometer is a gauge that measures and displays the instantaneous speed of a land vehicle. Now universally fitted to motor vehicles, they started to be available as options in the 1900s, and as standard equipment from about 1910 onwards. Speedometers for other vehicles have specific names...
to measure the speed they are moving.
See also
 Air speed
 Land speed
An object's speed across land is measured by difference in movement between the object and the land beneath it. Atmospheric pressure and aerodynamics must be considered when attempting to calculate possible speeds from the force applied.Units:...
 List of vehicle speed records
 Speedometer
A speedometer is a gauge that measures and displays the instantaneous speed of a land vehicle. Now universally fitted to motor vehicles, they started to be available as options in the 1900s, and as standard equipment from about 1910 onwards. Speedometers for other vehicles have specific names...
 Typical projectile speeds
 V speeds
In aviation, Vspeeds are standard terms used to define airspeeds important or useful to the operation of all aircraft including fixedwing aircraft, gliders, autogiros, helicopters, and dirigibles...