If we plot a graph between force and time, the area under the curve and time - axis gives the value of

Options

A. force per unit time
B. average force
C. impulse
D. rate of change of momentum

Explanation

To solve the question, we need to understand the relationship between force and time in a graph and what the area under the curve represents.

### Step-by-Step Solution:

1. **Understanding the Graph**:
- We are given a graph where the x-axis represents time and the y-axis represents force.

2. **Identifying the Area Under the Curve**:
- The area under the force-time graph (between the curve and the time-axis) represents a physical quantity.

3. **Relating Force and Momentum**:
- According to Newton's second law, force (F) is related to the rate of change of momentum (p) as follows:
\[ F = \frac{dp}{dt} \]
- Rearranging this gives us:
\[ dp = F \cdot dt \]

4. **Integrating Over Time**:
- If we integrate both sides over a time interval, we get:
\[ \int dp = \int F \cdot dt \]
- The left side gives us the change in momentum (Δp), and the right side gives us the area under the force-time graph.

5. **Conclusion**:
- Therefore, the area under the force-time graph is equal to the impulse (J), which is defined as the change in momentum:
\[ J = \Delta p \]
- Thus, the area under the curve of the force-time graph gives us the impulse.

### Final Answer:
The area under the curve of a force-time graph gives the value of **impulse**.

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