The position-time graphs for two students $A$ and $B$ returning from the school to their homes are shown in figure

$(A)$ $A$ lives closer to the school

$(B)$ $B$ lives closer to the school

$(C)$ $A$ takes lesser 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 position of a particle related to time is given by $x =\left(5 t ^2-4 t +5\right) m$. The magnitude of velocity of the particle at $t=2\,s$ will be $………..ms^{-1}$

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