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Two particles A and B are initially 20 m apart. A is behind B. Particle A starts moving with a uniform velocity of 5 m/s towards B. Particle B starting from rest has an acceleration of 1 m/s2 in the direction of velocity of A. The minimum distance between the particles is 1.5n(metres). Then n is ___

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Solution

Take the origin at the initial position of A and positive x-axis towards B. At a time t, xA and xB are the Co-ordinates of the particles. Gap = G = xBxA
G=(20+12×1×t2)(5t)
The gap is minimum when dGdt=0
t=5 seconds
Minimum gap =20+12×(5)25(5)=7.5m=1.5×5(m)

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