Final answer:
The area under a velocity-time graph represents the displacement of an object, distinguishing it from the slope of the graph, which indicates acceleration.
Step-by-step explanation:
The area under a velocity-time graph represents the displacement of an object. This is because displacement is calculated by finding the area under the line in a velocity vs. time graph. When the motion is at constant velocity, the graph will display a straight line, and the area under this line (which could be a rectangle or a trapezoid) corresponds to the object's displacement. If the graph shows a curve, the area under the curve still represents the total displacement over the time interval.
It should be noted that the slope of a velocity-time graph represents the acceleration, not the area under the graph. Therefore, the correct answer to the question of which quantity the area under a velocity-time graph represents is (a) displacement.