Area under speed-time curve gives

Options

A. distance
B. velocity
C. acceleration
D. none of these

Explanation

To solve the question regarding what the area under a speed-time curve represents, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Graph**:
- We start with a speed-time graph where the x-axis represents time (t) and the y-axis represents speed (v).

2. **Identifying the Area**:
- The area under the speed-time curve can be visualized as a series of rectangles (or a more complex shape depending on the graph) where the height of each rectangle corresponds to speed (v) and the width corresponds to a small time interval (dt).

3. **Calculating the Area**:
- The area of a small strip under the curve can be expressed as:
\[ \text{Area of strip} = v \cdot dt \]
- To find the total area under the curve from time \( t_1 \) to \( t_2 \), we integrate this expression:
\[ \text{Total Area} = \int_{t_1}^{t_2} v \, dt \]

4. **Relating Area to Distance**:
- We know that speed (v) is defined as the rate of change of distance (s) with respect to time (t):
\[ v = \frac{ds}{dt} \]
- Rearranging gives us:
\[ ds = v \, dt \]
- Therefore, integrating \( ds \) over the time interval gives us the total distance (s) traveled:
\[ s = \int_{t_1}^{t_2} v \, dt \]

5. **Conclusion**:
- Hence, the area under the speed-time curve represents the total distance traveled by the body during the time interval from \( t_1 \) to \( t_2 \).

### Final Answer:
The area under the speed-time curve gives the **total distance traveled** by the body.

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