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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 ahead of the car B, the driver of the car A applied the brake producing a uniform retardation a. There will be no collision when

A

`d lt ((v_1 - v_2)^2)/(2a)`

B

`d lt (v_1^2 - v_2^2)/(2a)`

C

`d gt ((v_1 - v_2)^2)/(2a)`

D

`d gt (v_1^2 - v_2^2)/(2a)`

Text Solution

Verified by Experts

The correct Answer is:
C
Initial relative velocity ` = v_1 - v_2`, Final relative velocity = 0
From `v^2 = u^2 - 2as implies 0 = (v_1 - v_2)^2 - 2 xx a xx s`
`implies s = ((v_1 - v_2)^2)/(2a)`
If the distance between two cars is .s. then collision will take place. To avoid collision `d gt s`
`therefore d gt ((v_1 - v_2)^2)/(2a)`
where d= actual initial distance between two cars.
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