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 :

An electron starting from rest has a velocity that increases linearly with the time that is $v = kt,$ where $k = 2m/{\sec ^2}$. The distance travelled in the first $3 \,seconds$ will be………..$m$

The velocity $(v)$ and time $(t)$ graph of a body in a straight line motion is shown in the figure. The point $S$ is at $4.333$ seconds. The total distance covered by the body in $6 \;s$ is$…….m$

A man in a car at location $Q$ on a straight highway is moving with speed $v$. He decides to reach a point $P$ in a field at a distance $d$ from highway (point $M$ ) as shown in the figure.Speed of the car in the field is half to that on the highway. What should be the distance $RM$, so that the time taken to reach $P$ is minimum?