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Two cars A and B are moving in same direction with the velocity 30m/s and 20m/s. When car A is at the distance of d behind the car B, the driver of the car applies a brakes producing retardation of 2m/s. There will be no collision when??????

Two cars A and B are moving in same direction with the velocity 30m/s and 20m/s. When car A is at the distance of d behind the car B, the driver of the car applies a brakes producing retardation of 2m/s. There will be no collision when??????

Grade:12th pass

1 Answers

Arun
25750 Points
6 years ago
For no collision the velocity of A must reduce to that of velocity of B.
VA = 30 m/s , VB = 20 m/s , a = - 2 m/s2
i.e. the relavitive final velocity of A with respect to B must be 0. Vr = 0
The relative initial velocity of A with respect to B is ( VA-VB )
The relative acceleration of A with respect to B is (-a - 0 ) = - a
Using the equation : v2= u2+ 2as
0 = ( VA-VB )2 + 2 × -a × s'
s' = ( VA-VB )2 / 2 a
= (30-20) 2 / 4
=25 m
 
Hence no collision occurs when d is greater than 25 m

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