Displacement v/s time graph in uniformly accelerated motion

Introduction:
In physics, uniformly accelerated motion refers to the motion of an object with a constant acceleration. This means that the object's velocity changes at a constant rate over time. The displacement v/s time graph for uniformly accelerated motion provides a visual representation of how the object's displacement changes with respect to time.

Explanation:
The displacement v/s time graph for uniformly accelerated motion is a parabola (option B). This can be understood by considering the key elements of uniformly accelerated motion.

1. Initial displacement:
At the beginning of the motion, when time (t) is zero, the object's displacement (s) is also zero. This point represents the origin of the graph.

2. Positive acceleration:
In uniformly accelerated motion, the acceleration is constant and can be either positive or negative. For the purpose of this explanation, let's consider positive acceleration. As time progresses, the object's velocity increases in a positive direction. Consequently, the object's displacement also increases at an increasing rate.

3. Increasing displacement:
As time increases, the object's displacement increases in a nonlinear fashion. This means that the displacement v/s time graph is not a straight line. Instead, it curves upwards, forming a parabolic shape.

4. Symmetry:
The displacement v/s time graph for uniformly accelerated motion is symmetric about the line passing through the point of origin and the maximum displacement. This symmetry occurs because the rate of change of displacement is the same in both the positive and negative time directions.

5. Maximum displacement:
The maximum displacement occurs when the object's velocity reaches zero. This occurs at the peak of the parabolic graph. Beyond this point, the object's velocity becomes negative, and the displacement continues to increase in the negative direction.

Conclusion:
In conclusion, the displacement v/s time graph for uniformly accelerated motion is a parabola. This graph represents the changing displacement of an object over time when subjected to a constant acceleration. It provides valuable information about the object's motion, including the direction and rate of change of displacement.