The distance covered by a moving body is directly proportional to the square to the time. The acceleration of the body is

Options

A. Increases
B. Remains constant
C. Is zero
D. Decreases

Answer

To solve the problem, we need to analyze the relationship between distance, time, and acceleration based on the information given.

### Step-by-Step Solution:

1. **Understanding the relationship**:
The problem states that the distance \( s \) covered by a moving body is directly proportional to the square of the time \( t \). This can be mathematically expressed as:
\[ s = k t^2 \]
where \( k \) is a constant of proportionality.

2. **Finding Velocity**:
To find the velocity, we differentiate the distance \( s \) with respect to time \( t \):
\[ v = \frac{ds}{dt} = \frac{d}{dt}(k t^2) \]
Using the power rule of differentiation, we get:
\[ v = k \cdot 2t = 2kt \]

3. **Finding Acceleration**:
Next, we differentiate the velocity \( v \) with respect to time \( t \) to find the acceleration \( a \):
\[ a = \frac{dv}{dt} = \frac{d}{dt}(2kt) \]
Since \( 2k \) is a constant, the differentiation gives:
\[ a = 2k \cdot \frac{d}{dt}(t) = 2k \cdot 1 = 2k \]

4. **Conclusion**:
The acceleration \( a \) is a constant value \( 2k \). Therefore, the acceleration of the body remains constant.

### Final Answer:
The acceleration of the body is constant.