The acceleration-time graph of a particle moving along a straight line is shown. At what time does the particle acquire its initial velocity? (in $s$)

The position-time graphs for two students $A$ and $B$ returning from the school to their homes are shown in the figure.
$(A)$ $A$ lives closer to the school.
$(B)$ $B$ lives closer to the school.
$(C)$ $A$ takes less time to reach home.
$(D)$ $A$ travels faster than $B$.
$(E)$ $B$ travels faster than $A$.
Choose the correct answer from the options given below:

The given graph shows the variation of velocity with displacement. Which one of the graphs given below correctly represents the variation of acceleration with displacement?

For the given displacement-time graph,what will the corresponding velocity-time graph look like?

The displacement $x$ of a particle in a straight line motion is given by $x = 1 - t - t^2$. The correct representation of the motion is $..............$.

The velocity $(v)$ versus displacement $(x)$ plot of a body moving along a straight line is as shown in the graph. The corresponding plot of acceleration $(a)$ as a function of displacement $(x)$ is