# Speed

Speed

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 traveled 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 .

Like velocity, speed has the dimensions of a length divided by a time; the SI unit 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 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 vacuum c = 299,792,458 meters per second, approximately 1079 million kilometers per hour (671,000,000 mph). Matter 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 velocity v, that is the derivative of the position r with respect to time:

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

If s is the length of the path traveled 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 traveled divided by the time duration.

Expressed in graphical language, the slope of a tangent line of a distance-time graph is the instantaneous speed, and the slope of a chord line of distance-time graph is the average speed over the time interval between the ends of the chord.

## Units

Units of speed include:

Conversions between common units of speed
m/s km/h mph knot ft/s
1 m/s = 1 3.6 2.236936 1.943844 3.280840
1 km/h = 0.277778 1 0.621371 0.539957 0.911344
1 mph = 0.44704 1.609344 1 0.868976 1.466667
1 knot = 0.514444 1.852 1.150779 1 1.687810
1 ft/s = 0.3048 1.09728 0.681818 0.592484 1

(Values in bold face are exact.)

## Examples of different speeds

Speed m/s ft/s km/h mph Notes
Approximate rate of continental drift 0.00000001 0.00000003 0.00000004 0.00000002 4 cm/year. Varies depending on location
Speed of a common snail 0.001 0.003 0.004 0.002 1 millimeter per second.
A brisk walk 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 101 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 36.1 118 130 81
Highest recorded human-powered speed 37.02 121.5 133.2 82.8 Sam Whittingham in a recumbent bicycle[1]
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 35,000 ft 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 1125 1235 768 Mach 1 by definition. 20 °C = 293 kelvin.
Muzzle velocity of an AK47 assault rifle bullet 710 2,330 2,600 1600
Official flight airspeed record 980 3,215 3,530 2,194
Space shuttle on re-entry 7,800 25,600 28,000 17,500
Escape velocity on Earth 11,200 36,700 40,000 25,000 11.2 km∙s−1
Average orbital speed of planet Earth 29,783 97,713 107,218 66,623
Speed of light in vacuum (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 meter.

Vehicles often have a speedometer to measure the speed they are moving.

## References

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Synonyms:

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• Speed — Speed, n. [AS. sp?d success, swiftness, from sp?wan to succeed; akin to D. spoedd, OHG. spuot success, spuot to succees, Skr. sph[=a] to increase, grow fat. [root]170b.] 1. Prosperity in an undertaking; favorable issue; success. For common speed …   The Collaborative International Dictionary of English

• speed — [spēd] n. [ME sped < OE spæd, wealth, power, success, akin to spowan, to prosper, succeed < IE base * spēi , to flourish, expand > SPACE, SPARE] 1. the act or state of moving rapidly; swiftness; quick motion 2. a) the rate of movement or …   English World dictionary

• Speed — Speed, v. t. 1. To cause to be successful, or to prosper; hence, to aid; to favor. Fortune speed us! Shak. [1913 Webster] With rising gales that speed their happy flight. Dryden. [1913 Webster] 2. To cause to make haste; to dispatch with… …   The Collaborative International Dictionary of English

• speed — [ spid ] n. m. et adj. • 1968; mot angl., proprt « vitesse » ♦ Anglic. fam. 1 ♦ Amphétamine, L. S. D. Prendre du speed. 2 ♦ Adj. Qui a pris des amphétamines. ♢ Très agité, excité. Elle est speed, la directrice ! speed [spid] n. m. et adj. ÉTYM.… …   Encyclopédie Universelle

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• speed — ► NOUN 1) the rate at which someone or something moves or operates. 2) rapidity of movement or action. 3) each of the possible gear ratios of a bicycle. 4) the light gathering power or f number of a camera lens. 5) the duration of a photographic… …   English terms dictionary

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