2.1.3—Displacement from the area under a velocity–time graph

Displacement over an interval is the integral ∫v dt, represented by the signed area under a velocity–time graph. Areas below the time axis are negative.

Split the graph at zero crossings or changes of shape, then add signed areas. Total distance uses absolute areas instead.

A triangular v–t graph with base 4 s and height 6 m s⁻¹ gives displacement 12 m if it stays above zero.

The area gives displacement, not automatically distance; a return trip can cancel signed areas.