The acceleration of a moving body can be found from

Options

A. area under velocity - time graph
B. area under displacement - time graph
C. slope of distance - time graph
D. slope of velocity - time graph

Explanation

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

### Step 1: Understand the Definition of Acceleration
Acceleration (a) is defined as the rate of change of velocity (v) with respect to time (t). Mathematically, this is expressed as:
\[ a = \frac{dv}{dt} \]

### Step 2: Identify the Relevant Graph
In this context, we will use a velocity-time (Vt) graph. The x-axis represents time (t), and the y-axis represents velocity (v).

### Step 3: Relate Acceleration to the Graph
In a Vt graph, the acceleration of the moving body can be determined by the slope of the graph. The slope of a curve at any point gives the instantaneous rate of change of velocity with respect to time.

### Step 4: Determine the Slope
For a straight line on the Vt graph, the slope can be calculated as:
\[ \text{slope} = \frac{\Delta v}{\Delta t} \]
This slope is equal to the acceleration (a).

### Step 5: Analyze the Options
Now, let's analyze the options given in the question:
1. Area under the Vt graph - This is incorrect because the area under a Vt graph gives displacement, not acceleration.
2. Area under the displacement-time graph - This is also incorrect as it relates to the distance covered, not acceleration.
3. Slope of the distance-time graph - This is incorrect because the slope of a distance-time graph gives velocity, not acceleration.
4. Slope of the velocity-time graph - This is correct as it gives the acceleration.

### Conclusion
Thus, the correct answer is that the acceleration of a moving body can be found from the slope of the velocity-time graph.

---