Area under a `(v - t)` graph represents a physical quantity which has the unit

Options

A. `m^(2)`
B. `m`
C. `m^(3)`
D. `ms^(-1)`

Explanation

To find the physical quantity represented by the area under a velocity-time (v-t) graph and its unit, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Graph**: The area under a velocity-time graph represents a physical quantity. In this case, it is the displacement (or distance) traveled by an object over a certain time period.

2. **Formula for Area**: The area under the v-t graph can be calculated using the formula:
\[ \text{Area} = \int V \, dt \]
This integral signifies that we are summing up the velocity over time, which gives us the total displacement.

3. **Units of Velocity and Time**:
- The unit of velocity (V) is meters per second (m/s).
- The unit of time (t) is seconds (s).

4. **Calculating the Units of Area**:
- When calculating the area, we multiply the unit of velocity by the unit of time:
\[ \text{Unit of Area} = \text{Unit of Velocity} \times \text{Unit of Time} = \text{(m/s)} \times \text{s} \]
- Simplifying this gives:
\[ \text{Unit of Area} = \text{m} \]
Thus, the unit of the area under the v-t graph is meters.

5. **Conclusion**: Therefore, the area under a velocity-time graph represents the displacement, and its unit is meters (m).

### Final Answer:
The area under a (v-t) graph represents the physical quantity of displacement, which has the unit of meters (m).

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