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 lt ((v_(1) + v_(2))^(2))/(a)`
B. `d gt ((v_(1) - v_(2))^(2))/(2a)`
C. `d gt ((v_(1) - v_(2))^(2))/(a)`
D. `d lt ((v_(1) - v_(2))^(2))/(a)`

Answer

B

Explanation

The velocity of train relative to good train `v_(1) - v_(2)` should become zero before the trains meet.
`:. V_(r)^(2) = u_(r)^(2) + 2a_(r) s_(r)`
`0 = (v_(1) - v_(2))^(2) - 2as`
`:. s = ((v_(1) - v_(2))^(2))/(2a)`
The trains will not collide if
`d ge s, " i.e.," d ge ((v_(1) - v_(2))^(2))/(2a)`