Speed

This article is about the property of moving bodies. For other uses, see Speed (disambiguation).

"Slow" and "Slowness" redirect here. For other uses, see Slow (disambiguation) and Slowness (disambiguation).

Speed
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.
Common symbols	v
SI unit	m/s, m s−1
Dimension	L T-1

Part of a series of articles about
Classical mechanics
${\vec {F}}=m{\vec {a}}$ Second law of motion
History Timeline
Branches Applied Celestial Continuum Dynamics Kinematics Kinetics Statics Statistical
Fundamentals Acceleration Angular momentum Couple D'Alembert's principle Energy kinetic potential Force Frame of reference Inertial frame of reference Impulse Inertia / Moment of inertia Mass Mechanical power Mechanical work Moment Momentum Space Speed Time Torque Velocity Virtual work
Formulations Newton's laws of motion Analytical mechanics Lagrangian mechanics Hamiltonian mechanics Routhian mechanics Hamilton–Jacobi equation Appell's equation of motion Udwadia–Kalaba equation Koopman–von Neumann mechanics
Core topics Damping (ratio) Displacement Equations of motion Euler's laws of motion Fictitious force Friction Harmonic oscillator Inertial / Non-inertial reference frame Mechanics of planar particle motion Motion (linear) Newton's law of universal gravitation Newton's laws of motion Relative velocity Rigid body dynamics Euler's equations Simple harmonic motion Vibration
Rotation Circular motion Rotating reference frame Centripetal force Centrifugal force reactive Coriolis force Pendulum Tangential speed Rotational speed Angular acceleration / displacement / frequency / velocity
Scientists Galileo Huygens Newton Kepler Horrocks Halley Euler d'Alembert Clairaut Lagrange Laplace Hamilton Poisson Daniel Bernoulli Johann Bernoulli Cauchy

In everyday use and in kinematics, the speed of an object is the magnitude of its velocity (the rate of change of its position); it is thus a scalar quantity. 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; the instantaneous speed is the limit of the average speed as the duration of the time interval approaches zero.

Speed has the dimensions of distance divided by time. The SI unit of speed is the metre per second, but the most common unit of speed in everyday usage is the kilometre per hour or, in the US and the UK, miles per hour. 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 a vacuum c = 7008299792458000000♠299792458 metres per second (approximately 7008299722222222222♠1079000000 km/h or 7008299963840000000♠671000000 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. In equation form, that is

$v={\frac {d}{t}},$

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, 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 ${\boldsymbol {v}}$, that is, the derivative of the position ${\boldsymbol {r}}$ with respect to time:

$v=\left|{\boldsymbol {v}}\right|=\left|{\dot {\boldsymbol {r}}}\right|=\left|{\frac {d{\boldsymbol {r}}}{dt}}\right|\,.$

If $s$ is the length of the path (also known as the distance) travelled until time $t$, the speed equals the time derivative of $s$:

$v={\frac {ds}{dt}}.$

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

$d={\boldsymbol {\bar {v}}}t\,.$

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

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. A point on the outside edge of a merry-go-round or 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 to the circumference 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 (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 (2π radians exactly). When a direction is assigned to rotational speed, it is known as rotational velocity or 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) 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

Main article: Conversion of units § Speed or velocity

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 = 7008299792458000000♠299792458 m/s).

Conversions between common units of speed

	m/s	km/h	mph	knot	ft/s
1 m/s =	1	3.6	7000223693600000000♠2.236936	7000194384400000000♠1.943844	7000328084000000000♠3.280840
1 km/h =	6999277778000000000♠0.277778	1	6999621371000000000♠0.621371	6999539957000000000♠0.539957	6999911344000000000♠0.911344
1 mph =	6999447040000000000♠0.44704	7000160934400000000♠1.609344	1	6999868976000000000♠0.868976	7000146666700000000♠1.466667
1 knot =	6999514444000000000♠0.514444	1.852	7000115077900000000♠1.150779	1	7000168781000000000♠1.687810
1 ft/s =	6999304800000000000♠0.3048	7000109728000000000♠1.09728	6999681818000000000♠0.681818	6999592484000000000♠0.592484	1

(Values in bold face are exact.)

Examples of different speeds

Main article: Orders of magnitude (speed)

Speed	m/s	ft/s	km/h	mph	Notes
Approximate rate of continental drift	6992100000000000000♠0.00000001	6992300000000000000♠0.00000003	6992400000000000000♠0.00000004	6992200000000000000♠0.00000002	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	Fastest kick recorded at 130 milliseconds from floor to target at 1 meter distance. Average velocity speed across kick duration
Sprint runners	12.2	40	43.92	27	Usain Bolt's 100 metres world record.
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 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 1 minute
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
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 7004106680000000000♠35000 ft (7004106680000000000♠10668 m) altitude
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	7003112500000000000♠1125	7003123500000000000♠1235	768	Mach 1 by definition. 20 °C = 293.15 kelvins.
Muzzle velocity of a 7.62x39mm cartridge	710	7003233000000000000♠2330	7003260000000000000♠2600	7003160000000000000♠1600	The 7.62×39mm round is a rifle cartridge of Soviet origin
Official flight airspeed record for jet engined aircraft	980	7003321500000000000♠3215	7003353000000000000♠3530	7003219400000000000♠2194	Lockheed SR-71 Blackbird
Space shuttle on re-entry	7003780000000000000♠7800	7004256000000000000♠25600	7004280000000000000♠28000	17,500
Escape velocity on Earth	7004112000000000000♠11200	7004367000000000000♠36700	7004400000000000000♠40000	7004250000000000000♠25000	11.2 km·s−1
Voyager 1 relative velocity to the Sun in 2013	7004170000000000000♠17000	7004558000000000000♠55800	7004612000000000000♠61200	7004380000000000000♠38000	Fastest heliocentric recession speed of any humanmade object. (11 mi/s)
Average orbital speed of planet Earth around the Sun	7004297830000000000♠29783	7004977130000000000♠97713	7005107218000000000♠107218	7004666230000000000♠66623
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.
Speed of light in vacuum (symbol c)	7008299792458000000♠299792458	7008983571056000000♠983571056	7009107925284800000♠1079252848	7008670616629000000♠670616629	Exactly 7008299792458000000♠299792458 m/s, by definition of the metre

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. 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?" 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

• Air speed
• Land speed
• List of vehicle speed records
• Typical projectile speeds
• Speedometer
• V speeds

References

• Richard P. Feynman, Robert B. Leighton, Matthew Sands. The Feynman Lectures on Physics, Volume I, Section 8-2. Addison-Wesley, Reading, Massachusetts (1963). ISBN 0-201-02116-1.