Read the given statements and select the correct option.
Statement 1: When the displacement of a body is directly proportional to the square of the time, then the body is moving with uniform acceleration.
Statement 2 : The slope of velocity-time graph with time axis gives acceleration.

Options

A. Both statements 1 and 2 are true and statement 2 is the correct explanation of statement 1.
B. Both statements 1 and 2 are true but statement 2 is not the correct explanation of statement 1.
C. Statement 1 is true but statement 2 is false.
D. Statement 1 is false but statement 2 is true.

Answer

To solve the question, we need to analyze both statements provided:

**Statement 1:** When the displacement of a body is directly proportional to the square of the time, then the body is moving with uniform acceleration.

**Statement 2:** The slope of the velocity-time graph with the time axis gives acceleration.

### Step-by-Step Solution:

1. **Understanding Statement 1:**
- The equation of motion for a body under uniform acceleration is given by:
\[ s = ut + \frac{1}{2} a t^2 \]
where \( s \) is the displacement, \( u \) is the initial velocity, \( a \) is the acceleration, and \( t \) is the time.
- If we consider the case where the initial velocity \( u = 0 \), the equation simplifies to:
\[ s = \frac{1}{2} a t^2 \]
- From this equation, we can see that displacement \( s \) is directly proportional to \( t^2 \) if \( a \) is constant. Therefore, if displacement is directly proportional to the square of the time, it implies that the body is moving with uniform acceleration.

2. **Understanding Statement 2:**
- The slope of a velocity-time graph represents acceleration. This is derived from the definition of acceleration:
\[ a = \frac{dv}{dt} \]
- In a velocity-time graph, the slope (rise over run) gives the change in velocity (rise) over the change in time (run), which is exactly the definition of acceleration.
- Therefore, Statement 2 is also true.

3. **Conclusion:**
- Both statements are true.
- However, Statement 2 does not explain Statement 1. Statement 1 is about displacement and its relation to time, while Statement 2 is about the velocity-time graph and acceleration.

### Final Answer:
Both statements are true, but Statement 2 is not the correct explanation of Statement 1. Thus, the correct option is:
- **Option 2:** Both Statement 1 and 2 are true, but Statement 2 is not the correct explanation of Statement 1.