What does the area under a velocity-time graph represent?

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

Answer: (C)

Area under a velocity-time graph represents displacement—the total change in position over the time interval. Velocity tells you how fast and in what direction position is changing, so adding up (integrating) velocity over time gives how far you have moved from the start.

If velocity is constant at 5 m/s for 3 seconds, the area is a rectangle with width 3 s and height 5 m/s, yielding 15 meters of displacement. When velocity changes, you sum the small areas under the curve to get the total displacement; if velocity becomes negative, those areas subtract, reflecting movement in the opposite direction. The units work out to meters, matching a change in position.

Other options don’t fit because time is the horizontal axis, not an area; speed is the magnitude of velocity (no direction) and isn’t described by area; and acceleration is the rate of change of velocity, which corresponds to the slope of the velocity-time graph, not the area.