The area under velocity-time graph for a particle in a given interval of time represnets

Options

A. velocity
B. acceleration
C. work done
D. Displacement does not tell the nature of the actual motion of a particle between the points.

Explanation

To solve the question regarding what the area under the velocity-time graph represents, we can follow these steps:

### Step 1: Understand the Velocity-Time Graph
- A velocity-time graph plots velocity on the y-axis and time on the x-axis. The shape of the graph can vary depending on the motion of the particle.

**Hint:** Recall that the y-axis represents velocity and the x-axis represents time.

### Step 2: Identify the Concept of Area Under the Curve
- The area under the curve in a velocity-time graph corresponds to the total displacement of the particle over the time interval considered. This is because displacement can be calculated as the integral of velocity with respect to time.

**Hint:** Remember that area can be calculated as length × width, and in this case, it relates to velocity and time.

### Step 3: Relate Area to Displacement
- When calculating the area under the velocity-time graph, if the graph is above the time axis, it represents positive displacement. If the graph is below the time axis, it represents negative displacement. The total area gives the net displacement.

**Hint:** Think about how positive and negative areas contribute to the overall displacement.

### Step 4: Conclusion
- Therefore, the area under the velocity-time graph for a particle in a given interval of time represents the displacement of the particle during that time interval.

**Hint:** Consider what displacement means in the context of motion and how it differs from distance traveled.

### Final Answer
The area under the velocity-time graph for a particle in a given interval of time represents **displacement**.