Netencyclo, The wikipedia mirror - The biggest multilingual encyclopedia : Speed

- Speed -

Speed :

Speed

From Wikipedia, the free encyclopedia

Jump to: navigation, search
 This article needs additional citations for verification.
Please help improve this article by adding reliable references. Unsourced material may be challenged and removed. (April 2007)
This article is about speed in physics. For other uses, see Speed (disambiguation).

Speed is the rate of motion, or equivalently the rate of change in position, often expressed as distance d traveled per unit of time t.

Speed is a scalar quantity with dimensions length/time; the equivalent 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 component of velocity.

In mathematical notation, it is simply:

v = \left|\frac {dx}{dt}\right|

Note that v is the variable for speed.

Objects that move horizontally as well as vertically (such as aircraft) distinguish forward speed and climbing speed.

Contents

[edit] Units

Units of speed include:

Mach 1 ≈ 343 ms-1 ≈ 1235 km/h ≈ 768 mph in dry air at sea-level pressure and 293 kelvin (See Speed of sound for more detail.)
c = 299,792,458 ms-1
1 m/s = 3.6 km/h
1 mph = 1.609 km/h
1 knot = 1.852 km/h = 0.514 ms-1

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

[edit] Average speed

Speed as a physical property represents primarily instantaneous speed. In real life we often use average speed (denoted |\tilde{v}|), 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:

|\tilde{v}| = \frac{\Delta l}{\Delta t}

Instantaneous speed defined as a function of time on interval [t0,t1] gives average speed:

|\tilde{v}| = \frac{\int_{t_0}^{t_1} |v|(t) \, dt}{\Delta t}

while instantaneous speed defined as a function of distance (or length) on interval [l0,l1] gives average speed:

|\tilde{v}| = \frac{\Delta l}{\int_{l_0}^{l_1} \frac{1}{|v|(l)} \, dl}

It is often intuitively expected, but incorrect, that going half a distance with speed | v | a and second half with speed | v | b, produces total average speed |\tilde{v}| = \frac{|v|_a + |v|_b}{2}; the correct value is |\tilde{v}| = \frac{2}{\frac{1}{|v|_a} + \frac{1}{|v|_b}}. 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 distribution function (either in time or on distance):

|v| \sim D_t\; \Rightarrow \; |\tilde{v}| = \int |v| D_t(|v|) \, dv
|v| \sim D_l\; \Rightarrow \; |\tilde{v}| = \frac{1}{\int \frac{D_l(|v|)}{|v|} \, dv}

[edit] Examples of different speeds

Below are some examples of different speed. See also main article Orders of magnitude (speed):

[edit] See also

Look up speed, swiftness in Wiktionary, the free dictionary.

[edit] References

[edit] External links

Wikiquote
Wikiquote has a collection of quotations related to:
Speed
v • d • e
Kinematics

← Integrate … Differentiate →

Displacement (Distance) | Velocity (Speed) | Acceleration | Jerk | Jounce

Speed - Related Items

Speed - In the news

© 2008 Netencyclo - Netencyclo Home - Terms of Service - Privacy Policy - Program Policies
Netencyclo, the Wikipedia mirror : the biggest multilingual free-content encyclopedia on the Internet. It uses material from the Wikipedia article Speed. All Wikipedia content is licensed under the GNU Free Documentation License (see details). Content on this web site is provided for informational purposes only. We accept no responsibility for any loss, injury or inconvenience sustained by any person resulting from information published on this site. We encourage you to verify any critical information with the relevant authorities.