$A$ bird flies to and fro between two cars which move towards each other with velocities $v_1 = 20\, m/s$ and $v_2 = 30\, m/s$. If the speed of the bird is $v_3 = 10\, m/s$ and the initial distance of separation between them is $d = 2\, km$,find the total distance covered by the bird until the cars meet. (in $, m$)

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 $\,s$)

$A$ 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?

$A$ 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.........$m/s$.

Two bodies start moving from the same point along a straight line with velocities $v_1 = 6 \, m/s$ and $v_2 = 10 \, m/s$,simultaneously. After what time will their separation become $40 \, m$?

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 $10\,s$?