The area under an acceleration-time graph giv | vedclass

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(D) The correct option is $D$.By definition,acceleration $a$ is the rate of change of velocity with respect to time,given by the formula $a = \frac{dv

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Change in velocity

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(D) The correct option is $D$.By definition,acceleration $a$ is the rate of change of velocity with respect to time,given by the formula $a = \frac{dv}{dt}$.Rearranging this equation,we get $dv = a \cdot dt$.To find the total change in velocity over a time interval from $t_1$ to $t_2$,we integrate both sides: $\Delta v = \int_{t_1}^{t_2} a \cdot dt$.Geometrically,the integral $\int a \cdot dt$ represents the area under the acceleration-time graph.Therefore,the area under the acceleration-time graph gives the change in velocity of the object.

The area under an acceleration-time graph gives:

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