Speed

Speed (symbol: ''v'') is the rate of Motion , or equivalently the rate of change of position, expressed as Distance ''d'' moved per Unit of Time ''t''.

Speed is a Scalar Quantity with Dimension s 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.

Units of speed include:

Metres Per Second , (symbol m/s), the SI Derived Unit

Kilometres Per Hour , (symbol km/h)

Miles Per Hour , (symbol mph)

Knot s ( Nautical Mile s per hour, symbol kt)

Mach , where Mach 1 is the Speed Of Sound ; Mach ''n'' is ''n'' times as fast.

Speed Of Sound

Speed Of Light in Vacuum (symbol ''c'') is one of the Natural Units

important conversions

::1 mph = 1.609 km/h
::1 knot = 1.852 km/h = 0.514 m/s

Vehicles often have a Speedometer to measure the speed.

The rate of change of speed with respect to time is termed Acceleration .

AVERAGE SPEED

Speed as a Physical Property represents primarily instantaneous speed. In real life we often use ''average speed'' (denoted

ilde{v}

), 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:

:

ilde{v} = rac{\Delta l}{\Delta t}.

Instantaneous speed defined as a function of Time on interval

t_1

gives average speed:

:

ilde{v} = rac{\int_{t_0}^{t_1} v(t) \, dt}{\Delta t}

while instant speed defined as a function of Distance (or Length ) on interval

l_1

gives average speed:

:

ilde{v} = rac{\Delta l}{\int_{l_0}^{l_1} rac{1}{v(l)} \, dl}

It is often intuitively expected that going half a distance with speed

v_{a}

and second half with speed

v_{b}

, produce total average speed

ilde{v} = rac{v_a + v_b}{2}

. The correct value is

ilde{v} = rac{2}{rac{1}{v_a} + rac{1}{v_b}}

(Note that the first is Arithmetic Mean while the second is Harmonic Mean ).

Average speed can be derived also from speed Distribution Function (either in time or on distance):

:

v \sim D_t\; \Rightarrow \; 	ilde{v} = \int v D_t(v) \, dv

v \sim D_l\; \Rightarrow \; 	ilde{v} = rac{1}{\int rac{D_l(v)}{v} \, dv}

CULTURAL SIGNIFICANCE

ek'vos'' is etymologically derived from ''---ok'u-'' "swift"), birds, especially raptors such as the Hawk , and cats, e.g. the Lynx (see e.g. Flos Duellatorum ). The swiftest land animal is the Cheetah , reaching running speeds of up to 110km/h (68 mph) for short distances. For sustained speed, the fastest land animal is the thoroughbred horse.

COMMON MOVING OBJECTS' SPEED

For human beings, an average Walking speed is about 3 mph (~5 km/h, 1.39m/s), although this depends heavily on factors such as height, weight, and age.

for average persons is about 10 mph (~16 km/h, 4.44 m/s ). Top athelets can dash at a speed of 23.03 mph (~36.85 km/h, 10.24 m/s) within a short distance like 200 Metres sprint.

Cycling : 12 mph (~20 km/h, 5.56 m/s)

Car : average 65 mph (~104 km/h, 28.9 m/s ) on highway

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Information About

Speed