The driver of a train moving at a speed ` v_(1)` sights another train at a disane ` d`, ahead of him moving in the same direction with a slower speed ` v_(2)`. He applies the brakes and gives a constant teradation ` a` to his train. Show that here will be no collision if ` d gt (v_(1) -v_(2))^(2) //2 a`.

Options

A. `d gt ((upsilon_(1)-upsilon_(2))/(2alpha))`
B. `d lt ((upsilon_(1)-upsilon_(2))^(2))/(2alpha)`
C. `d gt ((upsilon_(1)-upsilon_(2))^(2))/(2alpha)`
D. None of these

Answer

C

Explanation

Relative velocity of first train with respect to other
`(upsilon_(1)-upsilon_(2))`

where, `alpha` = relative retardation
`s=((upsilon_(1)-upsilon_(2))^(2))/(2alpha)`
For avoiding collision `d gt ((upsilon_(1)-upsilon_(2))^(2))/(2alpha)`