The area under a velocity-time graph represents

1. Analyze the question We need to know what physical quantity is given by the area between a velocity-time graph and the time axis.

2. Explain the concept Velocity = displacement ÷ time, so displacement = velocity × time. On a velocity-time graph, velocity is on the vertical axis and time is on the horizontal axis. The area of a strip under the graph is (height × width) = (velocity × time), which gives displacement (or distance, if the motion is in a straight line without changing direction).

3. Step-by-step check of the options

• A. Final velocity attained: This is read directly from the vertical axis at the end of the motion. It is not an area.
• B. Distance covered: Area = velocity × time = distance. ✔
• C. Acceleration: This is the slope (gradient) of the graph, not the area.
• D. Work done: Work is force × distance. It is not obtained from a velocity-time graph.

Example: A car moves at a constant 10 m/s for 5 s. The area under the graph is a rectangle: 10 × 5 = 50 m. This is the distance covered.

For a graph that rises uniformly from 0 to v in time t, the area is a triangle: ½ × t × v, which equals the distance in uniformly accelerated motion (s = ½vt).

4. Answer The area under a velocity-time graph represents distance covered (more precisely, displacement).

5. Tip Remember: "Slope = Acceleration, Area = Distance."

• Velocity-time graph: slope → acceleration; area → distance.
• Distance-time graph: slope → velocity.