graphs

Question

Area under velocity-time graph gives:

RankGuru · Accepted Answer

The instantaneous velocity $v$ is defined as the rate of change of displacement $s$:
$v = \frac{ds}{dt} \implies ds = v \, dt$
Integrating both sides over a time interval from $t_1$ to $t_2$:
$\int ds = \int_{t_1}^{t_2} v \, dt$
$s = 	ext{Area under the } v-t 	ext{ graph}$.
Note: If the velocity becomes negative, the 'area' below the axis is subtracted to give displacement. Total area (ignoring sign) gives distance.

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