(A):Displacement of a body is the signed sum of the area under velocity-time graph.
(R ):Displacement is a vector quantity.

Answer

To solve the question regarding the assertion and reason related to displacement, we will analyze both statements step by step.

### Step-by-Step Solution:

1. **Understanding the Assertion**:
- The assertion states that "Displacement of a body is the signed sum of the area under the velocity-time graph."
- Displacement is defined as the change in position of an object and can be calculated using the area under the velocity-time graph. The area above the time axis (positive velocity) contributes positively to displacement, while the area below the time axis (negative velocity) contributes negatively. Therefore, the assertion is **true**.

2. **Understanding the Reason**:
- The reason states that "Displacement is a vector quantity."
- Displacement indeed has both magnitude and direction, which qualifies it as a vector quantity. Thus, the reason is also **true**.

3. **Analyzing the Relationship**:
- While both the assertion and reason are true, we need to determine if the reason correctly explains the assertion.
- The assertion focuses on how to calculate displacement using the area under the velocity-time graph, while the reason merely states that displacement is a vector quantity. The reason does not provide a direct explanation for why the area under the graph represents displacement.

4. **Conclusion**:
- The assertion is true, and the reason is true, but the reason is not the correct explanation for the assertion. Therefore, we conclude that:
- Assertion (A) is true.
- Reason (R) is true, but does not explain (A).

### Final Answer:
- **Assertion (A)**: True
- **Reason (R)**: True, but does not explain (A)

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