If a body starts from rest, the time in which it covers a particular displacement with uniform acceleration is :

Options

A. inversely proportional to the square root of the displacement
B. inversely proportional to the square root of the displacement
C. directly proportional to the displacement
D. directly proportional to the square root of the displacement

Answer

To solve the problem, we will use the equations of motion. The body starts from rest and covers a particular displacement with uniform acceleration.

### Step-by-Step Solution:

1. **Identify Given Information**:
- Initial velocity (u) = 0 (since the body starts from rest)
- Displacement (s) = given (we need to find the time for this displacement)
- Acceleration (a) = constant (uniform acceleration)

2. **Use the Equation of Motion**:
The second equation of motion states:
\[ s = ut + \frac{1}{2} a t^2 \]
Since the initial velocity \( u = 0 \), the equation simplifies to:
\[ s = \frac{1}{2} a t^2 \]

3. **Rearranging the Equation**:
To find the time \( t \), we can rearrange the equation:
\[ s = \frac{1}{2} a t^2 \implies t^2 = \frac{2s}{a} \]

4. **Taking the Square Root**:
Taking the square root of both sides to solve for \( t \):
\[ t = \sqrt{\frac{2s}{a}} \]

5. **Conclusion**:
The time \( t \) is directly proportional to the square root of the displacement \( s \) when acceleration \( a \) is constant. Thus, we can conclude that:
\[ t \propto \sqrt{s} \]

### Final Answer:
The time in which the body covers a particular displacement with uniform acceleration is directly proportional to the square root of the displacement.