The following plots show variation of velocity (v), with time (t), of a ball thrown vertically upward, and falling back. Which of the following plots is/are correct?
Show Hint
A velocity-time graph for any object under constant acceleration must be a straight line. If the graph "bounces" back to the positive side (like plot B), it represents a Speed-time graph, not a Velocity-time graph.
To determine which plot correctly depicts the variation of velocity with time for a ball thrown vertically upwards and then falling back, we need to analyze the motion of the ball under gravity. Let's break down the motion:
When the ball is thrown upwards, its initial velocity is positive, and it decreases linearly over time as it moves upward against gravity until it reaches its maximum height. The velocity becomes zero at the maximum height.
After reaching the maximum height, the ball starts to fall back down, and its velocity increases linearly in the negative direction due to gravity.
The correct graph should show a straight line with a negative slope starting from a positive value, reaching zero, and then continuing with a negative value, indicating the change in direction.
In this case:
Plot A shows a constant velocity, which is incorrect for this scenario as the velocity changes over time.
Plot B depicts a velocity that increases positively and then decreases linearly, which suggests incorrect motion.
Plot C correctly shows the velocity decreasing linearly to zero and then increasing negatively, illustrating the deceleration and acceleration due to gravity.
Plot D and Plot E incorrectly illustrate motion with non-linear and inconsistent slopes.
Therefore, the correct plot that represents the velocity-time graph for a ball thrown vertically upward and falling back is Plot C only.
