The area under the curve of a velocity time graph represents

Step 1: Analyze the question We are asked what physical quantity is given by the area under a velocity-time (v-t) graph.

Step 2: Explain the concept Area under a graph = (y-axis quantity) × (x-axis quantity).

• y-axis: velocity (m/s)
• x-axis: time (s)

Area = velocity × time = (m/s) × s = m, which is a unit of length, so the area represents displacement (or distance covered).

Step 3: Check each option

• A. Acceleration: This is the slope (gradient) of a v-t graph, not the area.
• B. Distance covered: Area = velocity × time, with units in metres. This matches.
• C. Instantaneous speed: This is read directly from a point on the curve, not from the area.
• D. Time taken: Time is on the x-axis, so it is read off directly.
• E. Work done: This is the area under a force-distance graph, not a v-t graph.

Step 4: Worked example If a car moves at a constant 10 m/s for 5 s, the graph is a horizontal line. The area is a rectangle: 10 × 5 = 50 m. This is exactly the distance travelled, since distance = speed × time.

For a curve, the same idea applies: the area is found by splitting it into small strips (or by integration, ∫v dt).

Answer: B. Distance covered

(Strictly speaking, the area gives displacement, and it equals distance when motion is in one direction. This is why "distance covered" is the best option here.)

Exam tip: Remember these pairs:

• v-t graph: slope = acceleration, area = distance
• d-t graph: slope = velocity
• F-d graph: area = work done

Just check the units: multiply the axes to get the area, and divide them to get the slope.