Which statement is true about a speed-time graph?

• A. The height of the curve is distance
• B. The area under the curve is distance
• C. The slope is distance
• D. The value at a time is distance

Answer: (B)

In a speed-time graph, the vertical axis shows speed and the horizontal axis shows time. To find how far something has traveled, imagine adding up tiny distances over very small time intervals. Each little distance is speed at that moment times the tiny time interval, and summing all those pieces gives the total distance. That sum is exactly the area under the speed-time curve. The value at a single moment on the graph represents instantaneous speed, not distance, and the slope of the curve represents acceleration, not distance. The height of the curve is speed, so it wouldn’t directly represent distance by itself.