The slope of work-time curve at any instant gives

Options

A. energy
B. intensity
C. power
D. impulse

Answer

To solve the question, "The slope of the work-time curve at any instant gives," we will analyze the relationship between work, time, and power.

### Step-by-Step Solution:

1. **Understanding the Work-Time Graph**:
- A work-time graph plots work done (W) on the y-axis and time (t) on the x-axis. The curve represents how work changes over time.

2. **Finding the Slope**:
- The slope of a curve at any point is defined as the change in the y-value (work) divided by the change in the x-value (time). Mathematically, this is expressed as:
\[ \text{slope} = \frac{dW}{dt} \]
- Here, \(dW\) is the infinitesimal change in work, and \(dt\) is the infinitesimal change in time.

3. **Relating Slope to Power**:
- In physics, power (P) is defined as the rate at which work is done. This is mathematically represented as:
\[ P = \frac{dW}{dt} \]
- Therefore, the slope of the work-time graph, which is \(\frac{dW}{dt}\), represents power.

4. **Conclusion**:
- From the analysis, we conclude that the slope of the work-time curve at any instant gives the instantaneous power.

### Final Answer:
The slope of the work-time curve at any instant gives **power**.

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