A steel ball is released from rest a distance | vedclass

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(D) The area under a velocity-time graph represents the displacement of the object.In the given graph,area $X$ represents the displacement of the ball

Vedclass · Accepted Answer

The ball rises and falls through the same distance between the impact $1$ and $2$.

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(D) The area under a velocity-time graph represents the displacement of the object.In the given graph,area $X$ represents the displacement of the ball as it rises from the surface after the $1^{st}$ impact until it reaches its maximum height.Area $Y$ represents the displacement of the ball as it falls from that maximum height back to the surface before the $2^{nd}$ impact.Since the ball rises and falls through the same vertical distance between two consecutive impacts,the magnitude of the displacement for the upward motion must equal the magnitude of the displacement for the downward motion.Therefore,the areas $X$ and $Y$ are equal because the ball rises and falls through the same distance between the $1^{st}$ and $2^{nd}$ impact.

$A$ steel ball is released from rest a distance above a rigid horizontal surface and bounces several times. The diagram shows how its velocity varies with time. Which statement correctly explains why the areas $X$ and $Y$ are equal?

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