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The foot per second (plural feet per second) is a unit of both speed (scalar) and velocity (vector quantity, which includes direction). [1] It expresses the distance in feet (ft) traveled or displaced, divided by the time in seconds (s). [2] The corresponding unit in the International System of Units (SI) is the meter per second.
Sir Isaac Newton's 1687 Principia includes a computation of the speed of sound in air as 979 feet per second (298 m/s). This is too low by about 15%. [ 3 ] The discrepancy is due primarily to neglecting the (then unknown) effect of rapidly fluctuating temperature in a sound wave (in modern terms, sound wave compression and expansion of air is ...
Using this equation for an average speed of 80 kilometres per hour on a 4-hour trip, the distance covered is found to be 320 kilometres. Expressed in graphical language, the slope of a tangent line at any point of a distance-time graph is the instantaneous speed at this point, while the slope of a chord line of the same graph is the average ...
For example, in imperial units, the speed of light is approximately 186 282 miles per second, [Note 4] or roughly 1 foot per nanosecond. [ Note 5 ] [ 15 ] [ 16 ] In branches of physics in which c appears often, such as in relativity, it is common to use systems of natural units of measurement or the geometrized unit system where c = 1 .
The original Naismith's rule from 1892 says that one should allow one hour per three miles on the map and an additional hour per 2000 feet of ascent. [1] [4] It is included in the last sentence of his report from a trip. [1] [8] Today it is formulated in many ways. Naismith's 1 h / 3 mi + 1 h / 2000 ft can be replaced by:
From this derivative equation, in the one-dimensional case it can be seen that the area under a velocity vs. time (v vs. t graph) is the displacement, s. In calculus terms, the integral of the velocity function v(t) is the displacement function s(t). In the figure, this corresponds to the yellow area under the curve.
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In SI, this slope or derivative is expressed in the units of meters per second per second (/, usually termed "meters per second-squared"). Since the velocity of the object is the derivative of the position graph, the area under the line in the velocity vs. time graph is the displacement of the object. (Velocity is on the y-axis and time on the ...