Two trains '$A$' and '$B$' of length '$l$' and '$4l$' are travelling into a tunnel of length '$L$' on parallel tracks from opposite directions with velocities $108\,km/h$ and $72\,km/h$,respectively. If train '$A$' takes $35\,s$ less time than train '$B$' to cross the tunnel,then the length '$L$' of the tunnel is $...........\,m$. (Given $L = 60l$)

$A$ bead is moving in medium $1$ with a uniform speed of $1\, m/s$ for $2.5\, s$. Then it enters into air and falls freely under gravity for $2\, m$. Finally, it enters medium $2$ and immediately moves with uniform speed for $1.5\, s$. The total distance the bead has traveled is.........$m$ $(g = 10\, m/s^2)$: (in $.1$)

$A$ 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 $1\; s$. Plot the $x-t$ graph of his motion. How long (in $s$) does the drunkard take to fall into a pit $13\; m$ away from the start?

Choose the correct statement.

$Assertion$: $A$ body with constant acceleration always moves along a straight line.
$Reason$: $A$ body with constant acceleration may not speed up.

Which of the following statements are correct?
$(a)$ Average speed of a particle in a given time interval is never less than the magnitude of average velocity.
$(b)$ It is possible to have a situation in which $|d\vec{v}/dt| \neq 0$ but $d/dt|\vec{v}| = 0$.
$(c)$ The average velocity of a particle is zero in a time interval. It is possible that the instantaneous velocity is never zero in the interval.
$(d)$ The average velocity of a particle moving on a straight line is zero in a time interval. It is possible that the velocity is never zero in the interval. (Infinite accelerations are not allowed).