The velocity of a particle is $v = v _{0}+ gt + Ft ^{2}$. Its position is $x=0$ at $t=0$; then its displacement after time $( t =1)$ is :

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 :

Which of the following velocity-time graphs is physically not possible?

A particle moves along a straight line $OX$ . At a time $t$ (in seconds) the distance $x$ (in metres ) of the particle from $O$ is given by $x = 40 + 12t – {t^3}$.How long would the particle travel before coming to rest ?……….$m$