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.
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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:
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 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:
- meters per second (symbol m s−1 or m/s), the SI derived unit;
- kilometers per hour (symbol km/h);
- miles per hour (symbol 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 = 299,792,458 m/s).
| 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.
See also
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.
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