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Two cars A and B are travelling in the s...

Two cars A and B are travelling in the same direction with velocities `v_(1) and v_(2)" "(v_(1) gt v_(2))`. When the car A is at a distance d behind the car B, the driver of the car A applies the brake B, the driver of the car A applies the brake producing uniform retardation, a. There will be no collision when :

A

`d lt ((v_(1)-v_(2))/(2a))`

B

`d gt (v_(1)^(2)-v_(2)^(2))/(2a)`

C

`d gt (v_(1)-v_(2))^(2)/(2a)`

D

`d lt (v_(1)^(2)-v_(2)^(2))/(2a)`

Text Solution

Verified by Experts

The correct Answer is:
C
For same direction relative velocity `=abs(v_(1)-v_(2))`
`" Distance covered", d=(v_(1)-v_(2))^(2)/(2a)`
`" For no collision", d gt (v_(1)-v_(2))^(2)/(2a)`
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