Among the following,the velocity $(v)$ - time $(t)$ graph representing the motion of a vertically projected body is

The $x - t$ graph shown in the figure represents:

Which of the following velocity-time graphs shows a realistic situation for a body in motion?

$A$ train starting from rest accelerates uniformly for $100\,s,$ then comes to a stop with a uniform retardation in the next $200\,s.$ During the motion,it covers a distance of $3\,km.$ Choose the wrong option.

The displacement $x$ versus time graph is shown below. Analyze the following statements:
$(A)$ The average velocity during $0$ to $3\ s$ is $10\ m/s$.
$(B)$ The average velocity during $3$ to $5\ s$ is $0\ m/s$.
$(C)$ The instantaneous velocity at $t = 2\ s$ is $5\ m/s$.
$(D)$ The average velocity during $5$ to $7\ s$ and instantaneous velocity at $t = 6.5\ s$ are equal.
$(E)$ The average velocity from $t = 0$ to $t = 9\ s$ is zero.
Choose the correct answer from the options given below.

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?