# Speed: Map

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Speed is the rate of motion, or equivalently the rate of change of distance.

Speed is a scalar quantity with dimensions length/time; the equivalent vector quantity to speed is 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. Therefore, speed is always positive.

In mathematical notation, if an object traveling at constant speed moves a distance x in time t, its speed v is given by:
v = \frac {x}{t}.

In many situations, objects do not move at a constant speed. For example, if a car goes 60 miles in 2 hours, its average speed during that time is 30 miles per hour, but its instantaneous speed may have varied. For an object which is accelerating or decelerating, the instantaneous speed is given by
v = \left|\frac {dx}{dt}\right|,
where dx is the distance it travels in a very short period of time dt. If the object travels a total distance x in time t, its average speed over that time is given by
\bar{v} = \left|\frac {x}{t}\right|.

## Units

Units of speed include:
:c = 299,792,458 m/s

Important conversions between units of speed include:
:1 m/s = 3.6 km/h
:1 mph = 1.609 km/h
:1 knot = 1.852 km/h = 0.514 m/s