Given below are two statements: 

A car moves with a speed of $60$ km/h for $1$ hour in the east direction and with the same speed for $30$ min in the south direction. The displacement of the car from the initial position is:

A particle moves along a path $ABCD$ as shown in the figure. The magnitude of the displacement of the particle from $A$ to $D$ is:

1. $(5+10\sqrt{2})$m
2. $10$ m
3. $15\sqrt{2}$ m
4. $15$ m

A drunkard walking in a narrow lane takes $5$ steps forward and $3$ steps backward, followed again by $5$ steps forward and $3$ steps backward, and so on. Each step is $1$ m long and requires $1$ s. There is a pit on the road $13$ m away from the starting point. The drunkard will fall into the pit after:
1. $37$ s
2. $31$ s
3. $29$ s
4. $33$ s

The displacement $x$ of a particle moving in one dimension under the action of a constant force is related to time $t$ by the equation $t=\sqrt{x}+3,$ where $x$ is in meters and $t$ is in seconds. What is the displacement of the particle from $t=0~\text s$ to $t = 6~\text s?$

1. $0$
2. $12~\text m$
3. $6~\text m$
4. $18~\text m$

The figure gives the $(x\text-t)$ plot of a particle in a one-dimensional motion. Three different equal intervals of time are shown. The signs of average velocity for each of the intervals $1,$ $2$ and $3,$ respectively are: