The engine driver of a train moving at a speed `v_(1)` sights a freight train a distance d ahead, of him on the same track moving in the same direction with a slower speed `v_(2)`. He puts the brakets and gives his train a constant deceleration `alpha`. Then there will be no collision if

Options

A. `d lt ((v_(1)-v_(2))/(2alpha))`
B. `d lt ((v_(1)-v_(2))/(2alpha))`
C. `dgt((v_(1)-v_(2))^(2))/(2alpha)`
D. `d=(v_(1)-v_(2))/(2alpha)`

Answer

C

Explanation

For movement along same track in the same direction
Relative velocity `=(v_(1)-v_(2))" ":.` Distance covered `=((v_(1)-v_(2))^(2))/(2alpha)`
For no collision `d gt((v_(1)-v_(2))^(2))/(2alpha)`