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

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 a velocity-time graph represents, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Velocity-Time Graph**:
- A velocity-time graph plots velocity (v) on the y-axis and time (t) on the x-axis. The area under the curve of this graph represents a physical quantity.

2. **Identify the Area Under the Graph**:
- The area under the velocity-time graph can be calculated by finding the shape formed (which could be rectangles, triangles, or trapezoids) and using the appropriate area formulas.

3. **Relate Area to Displacement**:
- The area under the velocity-time graph corresponds to the displacement of the particle over the given time interval. This is because displacement is defined as the integral of velocity with respect to time.

4. **Formula for Displacement**:
- If the graph is a rectangle, the area (A) can be calculated as:
\[ A = \text{base} \times \text{height} = t \times v \]
- This means that the displacement (s) can be expressed as:
\[ s = v \times t \]
- For other shapes, the area can be calculated using respective area formulas.

5. **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.

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

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