The acceleration of a moving body can be found from

Options

A. Area under velocity-time graph
B. Area under distance-time graph
C. Slope of the velocity-time graph
D. Slope of distance-time graph

Answer

To find the acceleration of a moving body, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Acceleration**:
- Acceleration (a) is defined as the rate of change of velocity (v) with respect to time (t). Mathematically, it is expressed as:
\[ a = \frac{dv}{dt} \]
- Here, \( dv \) represents the change in velocity, and \( dt \) represents the change in time.

2. **Velocity-Time Graph**:
- A velocity-time graph is a graphical representation where the x-axis represents time and the y-axis represents velocity.
- The slope of this graph indicates how velocity changes over time.

3. **Calculating the Slope**:
- The slope of a line on a graph is calculated using the formula:
\[ \text{slope} = \frac{y_2 - y_1}{x_2 - x_1} \]
- In the context of a velocity-time graph:
- \( y_2 \) and \( y_1 \) are the velocities at two different times \( t_2 \) and \( t_1 \).
- Thus, we can write:
\[ \text{slope} = \frac{v_2 - v_1}{t_2 - t_1} \]

4. **Relating Slope to Acceleration**:
- From the previous step, we see that:
\[ \text{slope} = \frac{dv}{dt} \]
- Since \( \frac{dv}{dt} \) is the definition of acceleration, we conclude that:
\[ \text{slope} = a \]

5. **Conclusion**:
- Therefore, the acceleration of a moving body can be found from the slope of the velocity-time graph. The correct answer is option C.