The following plots show the variation of velocity $(v)$ with time $(t)$ for a ball thrown vertically upward and falling back. Which of the following plots is correct?

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

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 motion of a particle is described by the equation $x = a + bt^2$ where $a = 15 \, cm$ and $b = 3 \, cm/s^2$. Its instantaneous velocity at time $t = 3 \, s$ will be ........ $cm/s$.

Two trains, which are moving along different tracks in opposite directions, are put on the same track by mistake. On noticing the mistake, when the trains are $300 \, m$ apart, the drivers start slowing down the trains. The graphs given below show the decrease in their velocities as a function of time. The separation between the trains when both have stopped is: (in $ \, m$)

The following figures show velocity $v$ versus time $t$ curves. But only some of these can be realized in a particle. These are: