A particle starting from rest moves along a straight line with constant acceleration for this velocity displacement graph will have the form-

Options

A.
B.
C.
D.

Explanation

To determine the form of the velocity-displacement graph for a particle starting from rest and moving with constant acceleration, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Initial Conditions**: The particle starts from rest, which means its initial velocity \( U = 0 \).

2. **Use the Kinematic Equation**: For a particle moving with constant acceleration, the relationship between velocity \( V \), initial velocity \( U \), acceleration \( A \), and displacement \( S \) is given by the equation:
\[ V^2 = U^2 + 2AS \]
Since \( U = 0 \), the equation simplifies to:
\[ V^2 = 2AS \]

3. **Rearranging the Equation**: We can rearrange this equation to express \( V \) in terms of \( S \):
\[ V^2 = 2AS \implies V = \sqrt{2AS} \]
This shows that \( V \) is proportional to the square root of \( S \).

4. **Identifying the Graph Type**: The equation \( V = \sqrt{2AS} \) indicates that the graph of \( V \) versus \( S \) will not be a straight line. Instead, it will be a curve. Specifically, since \( V \) increases with \( S \) and is proportional to the square root of \( S \), the graph will be a parabola opening upwards.

5. **Conclusion**: Therefore, the velocity-displacement graph for a particle starting from rest and moving with constant acceleration will have a parabolic shape that opens upwards.

### Final Answer:
The velocity-displacement graph will be a parabola opening upwards.

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