Question

Two cars a and b are moving in same direction with velocity 30m/s and 20 m/s

Answer 1

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

@skb

Answer 2

Here Va=30m/s, Vb=20m/s

Vb-Va=30-20=10m/s

retardation=2m/s^2

by using the formula of retardation,

s=u^2/2a

s=10^2/2×2

s=100/4

s=25m

Hence there will be no collision when d>25m

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