Assertion : For a particle, acceleration-time graph gives the velocity.
Reason : Rate of change of velocity is acceleration.

Options

A. If both assertion and reason are trure and reason is the correct explanation of assertion.
B. If both assertion and reason are true but reason is not the correct explanations of assertion.
C. If assertion is true but reason is false.
D. If both assertion and reason is false

Answer

### Step-by-Step Solution

1. **Understanding the Assertion and Reason**:
- **Assertion**: For a particle, the acceleration-time graph gives the velocity.
- **Reason**: The rate of change of velocity is acceleration.

2. **Analyzing the Reason**:
- The reason states that acceleration is defined as the rate of change of velocity with respect to time. Mathematically, this is expressed as:
\[ a = \frac{dv}{dt} \]
- This statement is true. It indicates how velocity changes over time.

3. **Understanding the Acceleration-Time Graph**:
- An acceleration-time graph plots acceleration (a) on the y-axis against time (t) on the x-axis.
- The area under the acceleration-time graph represents the change in velocity (Δv) over a specific time interval.

4. **Relating Area Under the Graph to Velocity**:
- If we consider a time interval from \( t_1 \) to \( t_2 \), the area under the acceleration-time graph can be calculated as:
\[ \text{Area} = \int_{t_1}^{t_2} a \, dt = \Delta v \]
- This means that the area under the curve gives us the change in velocity during that time interval.

5. **Using the Equation of Motion**:
- According to the equations of motion, we have:
\[ v = u + at \]
- If we consider the initial velocity \( u = 0 \), then:
\[ v = at \]
- This shows that the final velocity is directly related to the acceleration and the time for which it acts.

6. **Conclusion**:
- The assertion that the acceleration-time graph gives velocity is correct because the area under the graph provides the change in velocity.
- The reason is also correct, but it does not directly explain why the assertion is true. Therefore, both statements are correct, but the reason is not a correct explanation of the assertion.

### Final Answer:
- Both the assertion and reason are correct, but the reason is not a correct explanation of the assertion. Thus, the correct option is **B**.