The figure shows the position-time $(x-t)$ graph of the motion of two boys $A$ and $B$ returning from school $O$ to their homes $P$ and $Q$ respectively. Which of the following statements is true?

The motion of an airplane is represented by a velocity-time graph as shown below. The distance covered by the airplane in the first $30.5 \ s$ is . . . . . . $km$.

$A$ train starting from rest accelerates uniformly for $100\,s,$ then comes to a stop with a uniform retardation in the next $200\,s.$ During the motion,it covers a distance of $3\,km.$ Choose the wrong option.

Consider a car initially at rest, starts to move along a straight road first with acceleration $5 \ m \ s^{-2}$, then with uniform velocity and finally, decelerating at $5 \ m \ s^{-2}$, before coming to a stop. Total time taken from start to end is $t = 25 \ s$. If the average velocity during that time is $72 \ km \ hr^{-1}$, the car moved with uniform velocity for a time of: (in $s$)

The displacement-time graph for two particles $A$ and $B$ is as follows. The ratio $\frac{v_A}{v_B}$ is

The velocity $v$ of a body moving along a straight line varies with time $t$ as $v = 2 t^2 e^{-t}$,where $v$ is in $m/s$ and $t$ is in $s$. The acceleration of the body is zero at $t =$