Two trains,one of length $100 \, m$ and another of length $125 \, m$,are moving in mutually opposite directions along parallel lines. They meet each other,each with a speed of $10 \, m/s$. If their accelerations are $0.3 \, m/s^2$ and $0.2 \, m/s^2$ respectively,then the time they take to pass each other will be ......... $s$.

$A$ bus is moving with a velocity $10\, ms^{-1}$ 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? ......... $ms^{-1}$

$A$ train is running at a constant speed of $90 \,km/h$ on a straight track. $A$ person standing on the top of a bogie moves in the direction of motion of the train such that he covers $1 \,m$ on the train each second. The speed of the person with respect to the ground is .........

$A$ $210 \ m$ long train is moving due North at a speed of $25 \ m/s$. $A$ small bird is flying due South a little above the train with a speed of $5 \ m/s$. The time taken by the bird to cross the train is $........ \ s$.

Two skaters $P$ and $Q$ are skating towards each other. Skater $P$ throws a ball towards $Q$ every $5 \,s$ such that it always leaves her hand with speed $2 \,ms^{-1}$ with respect to the ground. Consider two cases:
$(I)$ $P$ runs with speed $1 \,ms^{-1}$ towards $Q$,while $Q$ remains stationary.
$(II)$ $Q$ runs with speed $1 \,ms^{-1}$ towards $P$,while $P$ remains stationary.
Note that irrespective of the speed of $P$,the ball always leaves $P$'s hand with speed $2 \,ms^{-1}$ with respect to the ground. Ignore gravity. At what intervals will the balls be received by $Q$?

At a metro station, a girl walks up a stationary escalator in $20 \,s$. If she remains stationary on the escalator, then the escalator takes her up in $30 \,s$. The time taken by her to walk up on the moving escalator will be (in $\,s$)