Definitions
Nearby Words

# Speed

[speed]
Speed, John, 1552?-1629, English historian and cartographer. He abandoned his trade as a tailor to engage in mapmaking. Many of his maps of parts of England and Wales were published in The Theatre of the Empire of Great Britain (1611). His major work, The History of Great Britain, and his Genealogies Recorded in Sacred Scripture were published c.1611; they are based largely on earlier work.
speed, change in distance with respect to time. Speed is a scalar rather than a vector quantity; i.e., the speed of a body tells one how fast the body is moving but not the direction of the motion. If during time t a body travels over a distance s, then the average speed of that body is equal to s/t. The speed and direction of a body's motion together determine the body's velocity.

Sport of racing on ice skates. The blade of the speed skate is longer and thinner than that of the hockey or figure skate. Two types of track are used in international competition. The long track is a 400-m (about one-quarter mile) flattened oval (straight sides and curved ends) on which two skaters race simultaneously. In long track the race is against the clock rather than the opponent. The short track, a more recent development, is a 111-m (364-ft) oval on which four to six skaters race during each heat. Short track is a race to the finish line. Long-track speed skating was included in the first Winter Olympics in 1924; short-track skating was added in 1992.

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:

$v = left|frac \left\{d\right\}\left\{t\right\}right|.$
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.

## 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

• 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.

## Average speed

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

$|tilde\left\{v\right\}| = frac\left\{Delta l\right\}\left\{Delta t\right\}$

Instantaneous speed defined as a function of time on interval $\left[t_0, t_1\right]$ gives average speed:

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

while instantaneous speed defined as a function of distance (or length) on interval $\left[l_0, l_1\right]$ gives average speed:

$|tilde\left\{v\right\}| = frac\left\{Delta l\right\}\left\{int_\left\{l_0\right\}^\left\{l_1\right\} frac\left\{1\right\}$

It is often intuitively expected, but incorrect, that going half a distance with speed $|v|_\left\{a\right\}$ and second half with speed $|v|_\left\{b\right\}$, produces total average speed $|tilde\left\{v\right\}| = frac$

. The correct value is $|tilde\left\{v\right\}| = frac\left\{2\right\}\left\{frac\left\{1\right\}$

(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):

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

## Examples of different speeds

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

• A brisk walk = 1.667 ms-1; 6 km/h; 3.75 mph (5.5 feet per second).
• Average orbital speed of planet Earth = 29,783 ms-1; 107,218.8 km/h; 66,622.67 mph.
• Official air speed record = 980.278 ms-1; 3,529 km/h; 2,188 mph.
• Olympic sprinters (average speed over 100 metres) = 10 ms-1; 36 km/h; 22.5 mph.
• Speed limit on a French autoroute = 36.111 ms-1; 130 km/h; 80 mph.
• Speed of a common snail = 0.001 ms-1; 0.0036 km/h; 0.0023 mph (1.02 millimeters per second).
• Taipei 101 observatory elevator = 1010 m/min ; 16.667 ms-1 ; 60.6 km/h; 37.6 mph
• the speed of sound in dry air at 20 °C (68 °F) is 343 ms-1 ; 1235 km/h, or 770 mph.
• Top speed of a Boeing 747-8 = 290.947 ms-1; 1047.41 km/h; 650.83 mph; (Mach 0.85)
• Space shuttle on re-entry = 7,777.778 ms-1; 28,000 km/h; 17,500 mph.