What does it mean if the area under the line on a velocity-time graph is equal to zero?

When the area under the line on a velocity-time graph is equal to zero, it indicates that the object has not traveled any distance during the time interval being considered. The area under the velocity-time graph represents the distance traveled; therefore, if this area is zero, it signifies that there has been no net movement.

If the velocity is zero for the entire duration, the object remains at rest, meaning it does not change its position. This scenario could occur if the object was stationary or if it oscillated back and forth but returned to its original position, resulting in no net distance traveled.

The other options do not adequately describe the implications of a zero area under the curve. Negative acceleration relates to the object's speed decreasing over time but does not inherently imply a distance of zero. Changing direction suggests the velocity is nonzero but may have components that sum to zero over time. Constant motion would mean a non-zero velocity would be sustained, which would also indicate a positive area under the graph. Thus, the interpretation that the area equates to no distance traveled is accurate.