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Question

# Two cars A and B are travelling in the same direction with velocities v1 and v2 (v1>v2) respectively. When the car B is at a distance d ahead of the car A, the driver of the car A applied the brake producing a uniform retardation a. There will be no collision if

A
d(v1v2)22a
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B
dv21v222a
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C
d(v1v2)22a
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D
dv21v222a
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Solution

## The correct option is C d≥(v1−v2)22aTaking the direction of motion as positive direction, Initial relative velocity of car A w.r.t. B is urel=uA−uB=v1−v2 To avoid the collision, both cars will come to hault and hence there velocity becomes zero. Final relative velocity of car A w.r.t. B is vrel=vA−vB=0 Relative acceleration of car A w.r.t. to car B is arel=−a−0=−a To avoid collision d≥Srel(1) Where Srel is relative diaplacement of car A w.r.t. car B Srel=u2rel2a (∴vrel=0) Srel=u2rel2a=(v1−v2)22a Hence from equation (1) we get, d≥(v1−v2)22a

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