What is common in the two graphs given below?

$A$ particle shows a distance-time curve as given in the figure. The maximum instantaneous velocity of the particle is around the point:

$A$ 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?

The position $x$ of a particle with respect to time $t$ along the $x$-axis is given by $x = 9t^2 - t^3$,where $x$ is in metres and $t$ is in seconds. What will be the position of this particle when it achieves maximum speed along the $x$-direction?

What does $\dot x$ represent?

The position-time graph for a particle is shown in the figure. Starting from $t=0$,at what time $t$ (in seconds) is the average velocity zero?