$A$ person walks up a stalled escalator in $80 \,s$. When standing on the same escalator, now moving, he is carried up in $20 \,s$. The time taken by him to walk up the moving escalator is (in $\,s$)

Two parallel rail tracks run north-south. Train $A$ moves north with a speed of $54 \; km \; h^{-1},$ and train $B$ moves south with a speed of $90 \; km \; h^{-1}.$ What is the velocity of $B$ with respect to $A$?

$A$ ship is travelling due east at $10 \, km/hr$. $A$ second ship,heading $30^o$ east of north,is always due north of the first ship. The speed of the second ship in $km/hr$ is:

The width of the river is $1 \; km$. The velocity of the boat is $5 \; km/hr$. The boat covers the width of the river along the shortest possible path in $15 \; min$. The velocity of the river stream is:

On a two-lane road,car $A$ is travelling with a speed of $36 \; km/h$. Two cars $B$ and $C$ approach car $A$ in opposite directions with a speed of $54 \; km/h$ each. At a certain instant,when the distance $AB = AC = 1 \; km$,car $B$ decides to overtake car $A$ before car $C$ does. What minimum acceleration (in $m/s^2$) of car $B$ is required to avoid an accident?

If the velocities of particles $A$ and $B$ with respect to the ground are ${\overrightarrow v _A}$ and ${\overrightarrow v _B}$ respectively,then:
$(a)$ Write the formula for the velocity of $A$ with respect to $B$.
$(b)$ Write the formula for the velocity of $B$ with respect to $A$.
$(c)$ Is the relation ${\overrightarrow v _{AB}} = -{\overrightarrow v _{BA}}$ correct?