Velocity-time Graphs

A velocity-time graph plots instantaneous velocity on the vertical axis against time on the horizontal axis. The displacement over any interval equals the integral of velocity with respect to time, and graphically an integral corresponds to the area under the curve. Hence the area enclosed between the velocity-time line and the time axis directly gives the displacement of the object during that interval. The slope of the same graph, not its area, represents acceleration, since acceleration is the time derivative of velocity. The option 'acceleration' is therefore wrong because acceleration is read from the gradient, not the enclosed region. The option 'average speed' is wrong because average speed is a single ratio, not an area, and area carries units of velocity times time, which are units of length. The option 'rate of change of acceleration' is unrelated to either the area or the slope of this graph. This is a core NCERT graphical interpretation result. As a dimensional check, multiplying the velocity axis (m/s) by the time axis (s) yields metres, confirming the area must indeed be a displacement.