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

The area under a velocity-time graph represents the distance traveled by an object. In a velocity-time graph, the vertical axis represents velocity, while the horizontal axis represents time. When you calculate the area under the curve of this graph, you're essentially summing up all the small segments of distance the object covers over each time interval.

Since velocity is defined as the rate of change of position with respect to time, multiplying velocity (which is distance per unit time) by time gives you distance. Hence, whether the object is moving at a constant velocity or accelerating, the area under the graph reflects the total distance that has been traveled in that timeframe.

This understanding is fundamental to interpreting motion in physics and helps bridge concepts of speed and travel distance in practical applications.