In a velocity-time graph, to find displacement, why do we find the area of the region under the graph? 

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justaguide | College Teacher | (Level 2) Distinguished Educator

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Velocity is the displacement in unit time. If an object is displaced by d it time t the velocity `v = d/t` .

`v = d/t`

=> `d = v*t`

The displacement of the object is the product of time and velocity. When velocity is plotted against time, the area under the graph is the product of velocity and time which is the displacement. This is the reason why the area of the region under the time velocity graph is calculated to determine the displacement.