MHT CET 2021 Physics Solved Paper

(b) For no collision, the speed of car A should be reduced to vB before the cars meet, i.e. final relative velocity of car A with respect to car B is zero, i.e.
v‌relative ‌=0
Here, initial relative velocity, ur=vA−vB
Relative acceleration, ar=−a−0=−a
Let relative displacement be sr.
Thus, from third equation of motion, we get
v‌relative ‌2‌‌=ur2+2arsr=(vA−vB)2−2asr
⇒‌‌‌‌sr‌‌=‌

(vA−vB)2

2a

For no collision, s≤sr
i.e., s≤‌

(vA−vB)2

2a