Two parallel rail tracks run north-south. On one track train A moves noth with a speed of `54 km h^(-1)` and on the other track train B moves south with a speed of `90 km h^(-1)`. The velocity of train A with respect to train B is

Explanation

Let positive direaction of motion be from South to North.
Given, `v_(A)=+54 kmh^(-1) = 15 ms^(-1)`
`v_(B)=-90 kmh^(-1) = -25 ms^(-1)`
`therefore` The relative velocity of B w.r.t. A
`v_(BA)=v_(B)-v_(A)=-25-15=-40 ms^(-1)`
i.e., the train B appears to A to move with a speed of `40 ms^(-1)` from North to South.