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 distance/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:
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.
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
- 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-1
Vehicles often have a speedometer to measure the speed they are going.
Speed as a physical property
represents primarily instantaneous speed. In real life we often use average speed
), which is rate
of total distance
) and time
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:
Instantaneous speed defined as a function of time on interval gives average speed:
while instantaneous speed defined as a function of distance (or length) on interval gives average speed: