Speed
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2008-07-03T02:47:21Z
Autobogg
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/* Examples of different speeds */
{{refimprove|date=April 2007}}
{{otheruses1|speed in physics}}
'''Speed''' is the rate of [[Motion (physics)|motion]], or equivalently the rate of change in position, often expressed as [[distance]] ''d'' traveled per [[Units of measurement|unit]] of [[time]] ''t''.
Speed is a [[Scalar (physics)|scalar]] [[quantity]] with [[dimension]]s [[length|distance]]/[[time]]; the equivalent [[vector (spatial)|vector]] quantity to speed is known as [[velocity]]. Speed is measured in the same physical units of measurement as velocity, but does not contain the element of direction that velocity has. Speed is thus the [[magnitude (mathematics)|magnitude]] component of velocity.
In mathematical notation, it is simply:
:<math>v = \left|\frac {d}{t}\right|.</math>
Note that "v" is the variable for speed.
Objects that move horizontally as well as vertically (such as [[aircraft]]) distinguish '''[[V speeds|forward speed]]''' and '''[[V speeds|climbing speed]]'''.
==Units==
Units of speed include:
*[[meters per second]], (symbol ms<sup>-1</sup>; m/s), the [[SI derived unit]]
*[[kilometers per hour]], (symbol km/h)
*[[miles per hour]], (symbol m/h)
*[[knot (nautical)|knot]]s ([[nautical mile]]s per hour, symbol kt)
*[[Mach number|Mach]], where Mach 1 is the [[speed of sound]]; Mach ''n'' is ''n'' times as fast.
::Mach 1 ≈ 343 ms<sup>-1</sup> ≈ 1235 km/h ≈ 768 mph in dry air at sea-level pressure and 293 [[kelvin]] (See ''[[Speed of sound]]'' for more detail.)
*[[speed of light]] in [[vacuum]] (symbol ''c'') is one of the [[natural units]]
::''c'' = 299,792,458 ms<sup>-1</sup>
*Other important conversions
::1 m/s = 3.6 km/h
::1 mph = 1.609 km/h
::1 knot = 1.852 km/h = 0.514 ms<sup>-1</sup>
Vehicles often have a [[speedometer]] to measure the speed they are going.
==Average speed==
Speed as a [[physical property]] represents primarily instantaneous speed. In real life we often use ''average speed'' (denoted <math>|\tilde{v}|</math>), which is [[rate]] of total [[distance]] (or [[length]]) and [[time]] interval.
For example, if you go 60 miles in 2 hours, your ''average'' speed during that time is 60/2 = 30 miles per hour, but your instantaneous speed may have varied.
In mathematical notation:
:<math>|\tilde{v}| = \frac{\Delta l}{\Delta t}</math>
Instantaneous speed defined as a function of [[time]] on interval <math>[t_0, t_1]</math> gives average speed:
:<math>|\tilde{v}| = \frac{\int_{t_0}^{t_1} |v|(t) \, dt}{\Delta t}</math>
while instantaneous speed defined as a function of [[distance]] (or [[length]]) on interval <math>[l_0, l_1]</math> gives average speed:
:<math>|\tilde{v}| = \frac{\Delta l}{\int_{l_0}^{l_1} \frac{1}{|v|(l)} \, dl}</math>
It is often intuitively expected, but incorrect, that going half a distance with speed <math>|v|_{a}</math> and second half with speed <math>|v|_{b}</math>, produces total average speed <math>|\tilde{v}| = \frac{|v|_a + |v|_b}{2}</math>. The correct value is <math>|\tilde{v}| = \frac{2}{\frac{1}{|v|_a} + \frac{1}{|v|_b}}</math><br /> (Note that the first is a proper [[arithmetic mean]] while the second is a proper [[harmonic mean]]).
Average speed can be derived also from speed [[Probability density function|distribution function]] (either in time or on distance):
:<math>|v| \sim D_t\; \Rightarrow \; |\tilde{v}| = \int |v| D_t(|v|) \, dv</math>
:<math>|v| \sim D_l\; \Rightarrow \; |\tilde{v}| = \frac{1}{\int \frac{D_l(|v|)}{|v|} \, dv}</math>
== Examples of different speeds ==
Below are some examples of different speed. See also main article [[Orders of magnitude (speed)]]:
*Speed of a common [[snail]] = 0.001 ms<sup>-1</sup>; 0.0036 km/h; 0.0023 mph (1.02 millimeters per second).
*A brisk [[walk]] = 1.667 ms<sup>-1</sup>; 6 km/h; 3.75 mph (5.5 feet per second).
*[[Olympic Games|Olympic]] [[Sprint (race)|sprinters]] (average speed over 100 metres) = 10 ms<sup>-1</sup>; 36 km/h; 22.5 mph.
* [[Taipei 101]] observatory elevator = 1010 m/min ; 16.667 ms<sup>-1</sup> ; 60.6 km/h; 37.6 mph
*Speed limit on a [[France|French]] [[Freeway|autoroute]] = 36.111 ms<sup>-1</sup>; 130 km/h; 80 mph.
*Top cruising speed of a [[Boeing 747-8]] = 290.947 ms<sup>-1</sup>; 1047.41 km/h; 650.83 mph; ([[Mach]] 0.85)
*the [[speed of sound]] in dry air at 20 °C (68 °F) is 343 ms<sup>-1</sup> ; 1235 km/h, or 770 mph.
*Official [[air speed record]] = 980.278 ms<sup>-1</sup>; 3,529 km/h; 2,188 mph.
*[[Space shuttle]] on re-entry = 7,777.778 ms<sup>-1</sup>; 28,000 km/h; 17,500 mph.
*Average orbital speed of planet [[Earth]] = 29,783 ms<sup>-1</sup>; 107,218.8 km/h; 66,622.67 mph.
==See also==
{{Wiktionary|swiftness}}
*[[Air speed]]
*[[Land speed]]
*[[List of vehicle speed records]]
*[[Orders of magnitude (speed)]]
*[[Paul Virilio]]
*{{ml|Projectile|Typical_projectile_speeds|Typical projectile speeds}}
*[[V speeds]]
==External Links==
*[http://www.unitsconversion.com.ar/speedunitsconversion/ Online speed units conversion]
==References==
*Weisstein, Eric W. "Speed." From MathWorld--A Wolfram Web Resource. [http://mathworld.wolfram.com/Speed.html]
{{Kinematics}}
[[Category:Units of velocity|Units of velocity]]
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