A body starts from rest and then moves with uniform acceleration. Then.

Options

A. Its displacement is directly proportional to square of time
B. Its displacement is inversely proportion to the square of the time.
C. It may move along a circle.
D. It always moves in a straight line.

Explanation

To solve the problem step by step, we need to analyze the motion of a body that starts from rest and moves with uniform acceleration.

### Step-by-step Solution:

1. **Understanding Initial Conditions**:
- The body starts from rest, which means the initial velocity \( u = 0 \).

2. **Uniform Acceleration**:
- The body moves with uniform acceleration, meaning that the acceleration \( a \) is constant.

3. **Using the Equation of Motion**:
- We can use the equation of motion that relates displacement \( s \), initial velocity \( u \), time \( t \), and acceleration \( a \):
\[ s = ut + \frac{1}{2} a t^2 \]
- Since the initial velocity \( u = 0 \), the equation simplifies to:
\[ s = \frac{1}{2} a t^2 \]

4. **Analyzing the Relationship**:
- From the equation \( s = \frac{1}{2} a t^2 \), we can see that the displacement \( s \) is directly proportional to the square of the time \( t^2 \). This means:
\[ s \propto t^2 \]

5. **Conclusion about Motion**:
- Since the acceleration is constant and there is no change in the direction of velocity, the body moves in a straight line.

6. **Final Options**:
- Based on the analysis:
- Displacement is strictly proportional to \( t^2 \) (First option is correct).
- Displacement is not inversely proportional to \( t^2 \) (Second option is incorrect).
- The body does not necessarily move in a circle (Third option is incorrect).
- The body always moves in a straight line due to constant acceleration (Fourth option is correct).

### Final Answer:
The correct options are the first and fourth.

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