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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.)
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.
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.
For reversible (ideal) processes, the area under the T–s curve of a process is the heat transferred to the system during that process. [1] Working fluids are often categorized on the basis of the shape of their T–s diagram. An isentropic process is depicted as a vertical line on a T–s diagram, whereas an isothermal process is a horizontal ...
The vertical deviation of a point A on an elastic curve with respect to the tangent which is extended from another point B equals the moment of the area under the M/EI diagram between those two points (A and B). This moment is computed about point A where the deviation from B to A is to be determined.
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The main feature of thermodynamic diagrams is the equivalence between the area in the diagram and energy. When air changes pressure and temperature during a process and prescribes a closed curve within the diagram the area enclosed by this curve is proportional to the energy which has been gained or released by the air.
US stocks ended Friday in the red, closing out a lackluster week despite a year of historic highs. The “Magnificent Seven” group of high-performing tech stocks — Alphabet, Amazon, Apple ...