two cars A and B are moving in same direction with velocities 30m/s an

1.	two cars A and B are moving in same direction with velocities 30m/s and 20m/s . when car A is at a distance 'd ' behind the car B , the driver of car A applies brakes producing uniform retardation of 2m/s2. there will be no collision when ?
Answer» 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 relative 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

two cars A and B are moving in same direction with velocities 30m/s and 20m/s . when car A is at a distance 'd ' behind the car B , the driver of car A applies brakes producing uniform retardation of 2m/s2. there will be no collision when ?

Answer»

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 relative 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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