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 $\,s$)

$A$ $120\, m$ long train $A$ is moving with a speed of $20\, m/s$. $A$ train $B$ of length $130\, m$ is moving with a speed of $30\, m/s$ in the opposite direction. Calculate the time taken by the trains to cross each other. (in $, s$)

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

Ball $A$ is thrown vertically upward with a speed of $10 \, m/s$. At the same instant,another ball $B$ is released from rest at a height $h$. At time $t$,the speed of $A$ relative to $B$ is ...........

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

$A$ police party is moving in a jeep at a constant speed $v$. They see a thief at a distance $x$ on a motorcycle which is at rest. The moment the police see the thief, the thief starts moving with a constant acceleration $a$. Which of the following relations is true if the police are able to catch the thief?