The area under a velocity-time graph represents

Analyze the question: You are asked what physical quantity is given by the area between a velocity-time graph and the time axis.

Explain the concept: Velocity is the rate of change of displacement with time:

v = Δs / Δt, so Δs = v × Δt

On a velocity-time graph, v is on the vertical axis and t is on the horizontal axis. The area under the graph (height × width, or v × t) therefore gives displacement. If the velocity stays in one direction, this is equal to the distance travelled.

Step-by-step solution:

1. Look at the units of the area: velocity (m/s) × time (s) = metres (m).
2. Metres is a unit of length, so the quantity is distance (or displacement).
3. Check the other options: • A. Speed: read directly from the vertical axis, not from the area. • B. Acceleration: this is the slope (gradient) of the graph, not the area. • C. Moment: this is force × perpendicular distance, which has nothing to do with this graph. • D. Distance: matches the area, since v × t = distance.

Answer: D. distance

Strictly speaking, the area gives displacement, but among the options given, distance is the correct one.

Exam tip: Remember it this way: slope = acceleration, area = distance (for a velocity-time graph). For a distance-time graph, the slope gives velocity instead. Note that WASSCE often tests this pair of facts.