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foot per second (ft/s or ft/sec)

The foot per second (symbolized ft/s or ft/sec) is the unit of linear speed in the foot-pound-second ( fps ) or English system. This quantity can be defined in either of two senses: average or instantaneous.

Average linear speed is obtained by measuring the distance in feet that an object travels in a certain number of seconds, and then dividing the distance by the time. If s avg represents the average speed of an object (in feet per second) during a time interval t (in seconds), and the distance traveled in that time is equal to d (in feet), then:

s avg = d / t

Instantaneous linear speed is more difficult to intuit, because it involves an expression of motion over an "infinitely short" interval of time. Let p represent a specific point in time. Suppose an object is in motion at about that time. The average speed can be measured over increasingly short time intervals centered at p , for example:

[ p -4, p +4]
[ p -3, p +3]
[ p -2 , p +2]
[ p -1, p +1]
[ p -0.5, p +0.5]
[ p -0.25, p +0.25]
[ p - x , p + x ]

where the added and subtracted numbers represent seconds. The instantaneous speed, s inst , is the limit of the measured average speed as x approaches zero. This is a theoretical value, because it cannot be obtained except by inference from measurements made over progressively shorter time spans.

It is important to realize that speed is not the same thing as velocity. Speed is a scalar (dimensionless) quantity, while velocity is a vector quantity consisting of speed and direction. We might say a car is traveling at 60 ft/s, and this tells us its speed. Or we might say the car is traveling at 60 ft/s at a compass bearing of 25 degrees (north-by-northeast); this tells us its velocity. As with speed, we might specify either the average velocity over a period of time, or the instantaneous velocity at an exact moment in time.

The foot per second is often used by lay people when talking about speed, particularly in the United States. But scientists, and most people in other parts of the world, use the meter per second (m/s), which is the standard unit of speed in the International System of Units ( SI ).

Also see foot , second , International System of Units ( SI ), and Table of Physical Units .

This was last updated in March 2011

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