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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 x-axis. Multiplying the velocity by the time, the time cancels out, and only displacement remains.)
These relationships can be demonstrated graphically. The gradient of a line on a displacement time graph represents the velocity. The gradient of the velocity time graph gives the acceleration while the area under the velocity time graph gives the displacement. The area under a graph of acceleration versus time is equal to the change in velocity.
In the mathematical field of graph theory, a distance-transitive graph is a graph such that, given any two vertices v and w at any distance i, and any other two vertices x and y at the same distance, there is an automorphism of the graph that carries v to x and w to y. Distance-transitive graphs were first defined in 1971 by Norman L. Biggs and ...
It is the first time-integral of the displacement [3] [4] (i.e. absement is the area under a displacement vs. time graph), so the displacement is the rate of change (first time-derivative) of the absement. The dimension of absement is length multiplied by time.
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.
Displacement is the shift in location when an object in motion changes from one position to another. [2] For motion over a given interval of time, the displacement divided by the length of the time interval defines the average velocity (a vector), whose magnitude is the average speed (a scalar quantity).
Date/Time Thumbnail Dimensions User Comment; current: 01:22, 25 February 2007: 496 × 504 (111 KB) Stannered {{Information |Description=Example of a en:velocity vs. time graph, and the relationship between velocity v, en:displacement s, and en:acceleration a. Traced in en:Inkscape from an original drawn in en:Microsoft Paint. |Source=[[:
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