The area under a velocity vs. time graph equals which of the following?

The area under a velocity vs. time graph represents displacement. Displacement is a vector quantity that indicates the change in position of an object and takes into account both the magnitude and direction of movement.

When calculating displacement from a velocity vs. time graph, the area under the curve over a specific time interval gives the total change in position during that period. This is because velocity is defined as the rate of change of position with respect to time, so integrating or summing these rates over time directly provides the total displacement.

In contrast, while distance does relate to displacement, it does not account for direction and is thus a scalar quantity. Speed is the magnitude of velocity without direction and does not provide information about the area under the graph. Acceleration, while important in dynamics, relates to the change in velocity over time rather than the position itself. This distinction clarifies why the correct answer is displacement, as it directly correlates to the area under the velocity vs. time graph.