The distance between two particles is decreasing at the rate of $6 \,m/s$. If these particles travel with the same speeds and in the same direction,then the separation increases at the rate of $4 \,m/s$. The speeds of the particles are:

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 $10\,s$?

$A$ ball is dropped from the top of a building of height $80 \,m$. At the same instant,another ball is thrown upwards with a speed of $50 \,m/s$ from the bottom of the building. The time at which the balls will meet is ........ $s$.

$A$ car $A$ is travelling on a straight level road with a uniform speed of $60 \text{ km/h}$. It is followed by another car $B$ which is moving with a speed of $70 \text{ km/h}$. When the distance between them is $2.5 \text{ km}$,the car $B$ is given a deceleration of $20 \text{ km/h}^2$. After how much time will $B$ catch up with $A$ in hours?

$A$ student is standing at a distance of $50 \, m$ from the bus. As soon as the bus begins its motion with an acceleration of $1 \, m/s^2$,the student starts running towards the bus with a uniform velocity $u$. Assuming the motion to be along a straight road,the minimum value of $u$,so that the student is able to catch the bus is.........$m/s$.

$A$ bus starts moving with an acceleration of $2\,m/s^2$. $A$ cyclist,$96\,m$ behind the bus,starts moving simultaneously towards the bus at a constant speed of $20\,m/s$. After how many seconds will the cyclist be able to overtake the bus?