Speed

:For alternate uses, see special education or speed (disambiguation).

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.

Related Topics:
Physical property - Rate - Distance - Length - Time

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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.

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In mathematical notation:

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

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Instantaneous speed defined as a function of time on interval gives average speed:

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

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while instant speed defined as a function of distance (or length) on interval gives average speed:

Related Topics:
Distance - Length

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

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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).

Related Topics:
Arithmetic mean - Harmonic mean

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

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

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

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