The area under a velocity-time graph between two times represents what quantity?

• A. Displacement
• B. Velocity
• C. Speed
• D. Acceleration

Answer: (A)

The area under a velocity-time graph between two times shows how far the position has changed in that interval, i.e., the displacement. Velocity tells how quickly position changes per unit time, so adding up tiny bits of distance over small time steps (velocity × time) across the interval gives the total change in position. On the graph, that sum is represented by the area under the curve: positive velocity adds area (positive displacement), negative velocity subtracts area (negative displacement). The other options don’t fit this geometric picture: velocity is the instantaneous rate shown by the graph’s height, speed is the magnitude of velocity (not the area), and acceleration is the rate of change of velocity (the slope of the velocity-time graph), not the area.