$A$ person of height $1.6 \ m$ is walking away from a lamp post of height $4 \ m$ along a straight path on the flat ground. The lamp post and the person are always perpendicular to the ground. If the speed of the person is $60 \ cm \ s^{-1}$,the speed of the tip of the person's shadow on the ground with respect to the person is . . . $cm \ s^{-1}$.

State whether the following statements are true or false:
$(a)$ Velocity can change without a change in speed.
$(b)$ The total distance covered by a freely falling body in a given time is directly proportional to the time.
$(c)$ $A$ particle is a point object that possesses dimensions.

The driver of a bus moving with a velocity of $72 \ km/h$ observes a boy walking across the road at a distance of $50 \ m$ in front of the bus and decelerates the bus at $5 \ m/s^2$ by applying brakes and is just able to avoid an accident. The reaction time of the driver is (in $s$)

$A$ 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 $s$)

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 $L = 60l$)

Two stones are thrown up simultaneously from the edge of a cliff $240 \ m$ high with initial speeds of $10 \ m/s$ and $40 \ m/s$ respectively. Which of the following graphs best represents the time variation of the relative position of the second stone with respect to the first? (Assume stones do not rebound after hitting the ground and neglect air resistance,take $g = 10 \ m/s^2$)