# Speed

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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.

## Contents

### 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: