The area under the velocity-time graph for a particle moving in a straight line with uniform acceleration gives

The area under a velocity-time (v-t) graph represents the net displacement of a particle [1]. In physics, velocity is a vector quantity, meaning it accounts for both magnitude and direction. When calculating the area under the v-t curve, regions where the velocity is positive contribute to positive displacement, while regions with negative velocity (below the time axis) represent displacement in the opposite direction [1]. The algebraic sum of these areas yields the net displacement [1]. While the total area (treating all parts as positive) can represent the distance travelled, the standard physical interpretation of the integral of velocity with respect to time is displacement. For a particle moving with uniform acceleration, the v-t graph is a straight line, and the geometric area (such as a triangle or trapezium) directly corresponds to the displacement formula s = ut + ½at² [1].

Sources

1. [1] https://sathee.iitk.ac.in/pyqs/revision-notes/physics/class-11/motion-straight-line/