$A$ man on a rectilinearly moving cart,facing the direction of motion,throws a ball straight up with respect to himself.

$A$ particle is dropped from rest and another particle is thrown downward simultaneously with initial speed $u$. Then:

Two balls are projected upward simultaneously with speeds $40 \, m/s$ and $60 \, m/s$. The relative position $(x)$ of the second ball with respect to the first ball at time $t = 5 \, s$ is .......... $m$ [Neglect air resistance].

Two cars $A$ and $B$ are moving in the same direction with velocities $30 \, m/s$ and $20 \, m/s$. When car $A$ is at a distance $d$ behind car $B$,the driver of car $A$ applies brakes,producing a uniform retardation of $2 \, m/s^2$. There will be no collision when ......... $m$.

$A$ bus is moving with a velocity $10 \, m/s$ on a straight road. $A$ scooterist wishes to overtake the bus in $100 \, s$. If the bus is at a distance of $1 \, km$ from the scooterist,with what velocity should the scooterist chase the bus? (in $m/s$)

$A$ motor car moving at a speed of $72\, km/h$ cannot come to a stop in less than $3.0\, s$ while for a truck this time interval is $5.0\, s$. On a highway,the car is behind the truck,both moving at $72\, km/h$. The truck driver signals an emergency stop. At what minimum distance should the car be from the truck so that it does not collide with the truck? The human response time is $0.5\, s$.