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 ......... $s$.

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 $Q$?

$A$ 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 .........

Two trains $A$ and $B$,initially $120\, km$ apart,start moving towards each other on the same track with a velocity of $60\, km/hr$ each. At the moment of start,train $A$ blows a whistle,which reflects off train $B$ and subsequently reflects off train $A$,and so on. If the velocity of sound waves in air is $1200\, km/hr$,what is the total distance travelled by the sound waves before the trains crash (in $km$)?

What are the speeds of two objects if,when they move uniformly towards each other,they get $4\,m$ closer in each second and when they move uniformly in the same direction with the original speeds,they get $4.0\,m$ closer each $10\,s$?

Two cars $A$ and $B$ are travelling in the same direction with velocities $V_A$ and $V_B$ $(V_A > V_B)$. When the car $A$ is at a distance $S$ behind the car $B$,the driver of the car $A$ applies the brakes producing a uniform retardation $a$. There will be no collision when: