Quantity measured by the area occupied below the velocity-time graph:

The area occupied below a velocity-time graph represents a physical quantity known as displacement. Displacement is a vector quantity that measures the change in position of an object, taking into account both the magnitude and direction of the change. It is often represented graphically as the area under the curve on a velocity-time graph.

Explanation:

1. Velocity-Time Graph:
A velocity-time graph plots the velocity of an object on the y-axis and the time on the x-axis. The graph provides valuable information about the motion of the object, including its speed, direction, and acceleration.

2. Displacement:
Displacement is a vector quantity that describes the change in position of an object. It is different from distance, which only considers the magnitude of the change. Displacement takes into account both the magnitude and direction of the change in position.

3. Area Under the Curve:
The area under the curve on a velocity-time graph represents the displacement of an object. When an object is moving with a constant velocity, the velocity-time graph appears as a straight line. In this case, the displacement can be calculated by multiplying the velocity by the time interval.

4. Non-Uniform Motion:
In the case of non-uniform motion, where the velocity of an object is changing, the area under the curve can be divided into smaller sections. By calculating the area of each section and summing them up, the total displacement of the object can be determined.

5. Positive and Negative Displacement:
The displacement can be positive or negative, depending on the direction of the motion. If the area under the curve is above the x-axis, it represents positive displacement, indicating the object is moving in the positive direction. Conversely, if the area is below the x-axis, it represents negative displacement, indicating the object is moving in the negative direction.

Conclusion:
In summary, the area occupied below the velocity-time graph represents the displacement of an object. By calculating the area under the curve, taking into account the direction of the motion, we can determine the change in position of the object. Displacement is a significant physical quantity that helps us understand the motion and position of an object.