The graph of velocity vs Displacement for this situation will be a parabola.

Graph of Velocity vs. Displacement for a Particle with Constant Acceleration

The graph of velocity vs. displacement for a particle with constant acceleration can be divided into three distinct regions:

1. Initial Region:
At the beginning, the particle starts from rest, so the velocity is zero when the displacement is zero. As the displacement increases, the velocity also increases linearly. This region represents the particle's acceleration phase.

2. Constant Velocity Region:
After a certain displacement, the particle reaches a constant velocity. In this region, the velocity remains constant while the displacement continues to increase. This indicates that the particle is no longer accelerating and is moving with a constant speed.

3. Final Region:
At a certain displacement, the particle comes to a stop. This is represented by the point where the velocity drops back to zero. After this point, the particle starts moving in the opposite direction. In this region, the velocity becomes negative as the displacement continues to increase in the opposite direction. This indicates that the particle is decelerating or moving in the opposite direction.

Key Points:
- The graph initially shows a linear increase in velocity with displacement, representing the particle's acceleration phase.
- After reaching a certain displacement, the graph levels off to a constant velocity, indicating that the particle is moving at a constant speed.
- At the final point, the velocity drops back to zero, signifying the particle's stoppage before starting to move in the opposite direction.
- The negative slope after the point of zero velocity represents the particle's deceleration or movement in the opposite direction.
- The graph can be used to determine the acceleration, constant velocity, and displacement of the particle by analyzing the slope and shape of the curve.

Overall, the graph of velocity vs. displacement for a particle with constant acceleration provides valuable information about the particle's motion, including its acceleration phase, constant velocity phase, and deceleration phase. Analyzing the graph can help in understanding the particle's behavior and determining key parameters related to its motion.