What does the area enclosed by the acceleration-time graph for any time interval represent?

$A$ particle of unit mass undergoes one-dimensional motion such that its velocity varies according to $v(x) = \beta x^{-2n}$,where $\beta$ and $n$ are constants and $x$ is the position of the particle. The acceleration of the particle as a function of $x$ is given by:

Draw the $x-t$ graph for an object moving with zero acceleration.

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?

The velocity-displacement graph of a particle is shown in the figure. The acceleration-displacement graph of the same particle is represented by:

The motion of an airplane is represented by a velocity-time graph as shown below. The distance covered by the airplane in the first $30.5 \ s$ is . . . . . . $km$.