$A$ 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 $, m$)

$A$ bus is moving with a speed of $10\; m/s$ 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 speed should the scooterist chase the bus? (in $m/s$)

$A$ man is at a distance $d$ behind a bus. The bus starts from rest and moves away from the man with a constant acceleration $a$. At the same time,the man starts running towards the bus with a constant velocity $v$. Which of the following statements are correct?

$A$ thief is running away on a straight road in a jeep moving with a speed of $9 \, m/s$. $A$ policeman chases him on a motorcycle moving at a speed of $10 \, m/s$. If the instantaneous separation between the jeep and the motorcycle is $100 \, m$,how long will it take for the policeman to catch the thief?

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

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: