A graph is drawn between velocity and time for the motion of a particle. The area under the curve between the time intervals`t_1 and t_2` gives

Options

A. Momentum of the particle
B. Displacement of the particle
C. Acceleration of the particle
D. Change in velocity of the particle

Explanation

To solve the question regarding the area under the velocity-time graph between the time intervals \( t_1 \) and \( t_2 \), we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Graph**:
- The graph in question is a velocity-time graph where the y-axis represents velocity (v) and the x-axis represents time (t).

2. **Identify the Area Under the Curve**:
- The area under the curve between the time intervals \( t_1 \) and \( t_2 \) represents a physical quantity.

3. **Relate Area to Displacement**:
- In physics, the area under a velocity-time graph gives the displacement of the particle. This is because displacement can be calculated as the integral of velocity with respect to time.
- Mathematically, this can be expressed as:
\[ \text{Displacement} = \int_{t_1}^{t_2} v \, dt \]
- This integral represents the area under the curve from \( t_1 \) to \( t_2 \).

4. **Conclusion**:
- Therefore, the area under the velocity-time graph between the time intervals \( t_1 \) and \( t_2 \) gives the displacement of the particle.

### Final Answer:
The area under the curve between the time intervals \( t_1 \) and \( t_2 \) gives the **displacement of the particle**.