# Speed

## Etymology

Middle English spede, from Old English spēd; akin to Old High German spuot prosperity, speed, Old English spōwan to succeed, Latin spes hope, Lithuanian spėti to be in time

For lessons on the related topic of Acceleration, follow this link.

## Definitions

Speed of light from Earth to the Moon.
• 1 archaic : prosperity in an undertaking : success
• 2 a : the act or state of moving swiftly : swiftness b : rate of motion: as (1) : velocity 1 (2) : the magnitude of a velocity irrespective of direction c : impetus
• 3 : swiftness or rate of performance or action : velocity 3a
• 4 a : the sensitivity of a photographic film, plate, or paper expressed numerically b : the light-gathering power of a lens or optical system c : the time during which a camera shutter is open
• 5 : a transmission gear in automotive vehicles or bicycles —usually used in combination <a ten-speed bicycle>
• 6 : someone or something that appeals to one's taste <just my speed>
• 7 : methamphetamine; also : a related stimulant drug and especially an amphetamine

## Description

In kinematics, the instantaneous speed of an object (denoted v) is the magnitude of its instantaneous velocity (the rate of change of its position); it is thus the scalar equivalent of velocity. 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 certain countries, the mile per hour.

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 (671 million miles) per hour. Matter cannot quite reach the speed of light, as this would require an infinite amount of energy.[https://en.wikipedia.org/wiki/Speed

The instantaneous speed v is defined as the magnitude of the instantaneous 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: