The area under force-displacement curve represents

Options

A. velocity
B. acceleration
C. impulse
D. work done

Explanation

To solve the question regarding what the area under the force-displacement curve represents, we can follow these steps:

### Step 1: Understand the Axes
- The x-axis represents displacement (x).
- The y-axis represents force (F).

**Hint:** Identify the variables represented on the axes of the graph.

### Step 2: Recognize the Curve
- The curve on the graph represents a function of force as a function of displacement, denoted as F(x).

**Hint:** The shape of the curve can vary depending on the relationship between force and displacement.

### Step 3: Concept of Area Under the Curve
- The area under the curve between two points (x1 and x2) can be calculated using integration. The area can be expressed mathematically as:
\[ \text{Area} = \int_{x_1}^{x_2} F(x) \, dx \]

**Hint:** Recall that integration is a way to sum up small areas under the curve.

### Step 4: Relate Area to Work Done
- The work done (W) when a force is applied over a displacement can be defined as:
\[ W = \int_{x_1}^{x_2} F(x) \, dx \]
- This shows that the work done is equal to the area under the force-displacement curve.

**Hint:** Remember that work is defined as force applied over a distance.

### Step 5: Conclusion
- Therefore, the area under the force-displacement curve represents the work done by the force as the object moves from displacement x1 to x2.

**Final Answer:** The area under the force-displacement curve represents the work done.