$A$ person wearing a parachute jumps off a plane from a height of $2 \ km$ from the ground and falls freely for $20 \ m$ before his parachute opens. After his parachute opens,if he continues to move uniformly with the velocity attained due to his freefall,the total time taken by the person to reach the ground is (Acceleration due to gravity $= 10 \ m/s^2$) (in $s$)

$A$ cyclist starts from the centre $O$ of a circular park of radius $1\; km$,reaches the edge $P$ of the park,then cycles along the circumference,and returns to the centre along $QO$ as shown in Figure. If the round trip takes $10 \;min$,what is the
$(a)$ net displacement,
$(b)$ average velocity,and
$(c)$ average speed of the cyclist?

$A$ bogie of a uniformly moving train is suddenly detached from the train and stops after covering some distance. What is the relation between the distance covered by the bogie and the distance covered by the train in the same time?

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).

$A$ 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?

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 $L = 60l$)