Displacement on a Velocity-time Graph

The displacement of an object is given by the area under its velocity-time graph. This is because displacement = velocity × time, and each small strip under the graph has an area equal to velocity × time interval.For constant velocity the area is a rectangle. For uniform acceleration the area is a triangle or a trapezium. The area of a trapezium is ½(a + b)h, where a and b are the parallel sides and h is the perpendicular distance between them. On a velocity-time graph, a and b are the initial and final velocities and h is the time.For example, an object that accelerates uniformly from 4.0 m s^-1 to 12 m s^-1 in 5.0 s has a displacement of ½(4.0 + 12) × 5.0 = 40 m. When the line is curved, the area is estimated by counting squares.Areas below the time axis represent displacement in the opposite direction and count as negative. To find the total distance travelled, add all the areas as positive values instead.