Q.

A cat, on seeing a rat at a distance d = 5 m, starts with velocity u=5ms−1 and moves with acceleration α=2.5ms−2 in order to catch it, while the rat with acceleration β starts from rest. For what maximum value of β will the cat overtake the rat? (in ms-2)

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answer is 5.

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Detailed Solution

For rat S=12βt2  ……..(i) For cat S+d=ut+12αt2 …………(ii)Putting the value of S from Eq. (i) in Eq. (ii),     (α−β)t2+2ut−2d=0t=2u±4u2−8d(β−α)2(β−α) For t to be real, u22d≥(β−α)∴ βmax=α+u22dSubstituting a, d and u, we getβ=2.5+522×5=2.5+2.5=5ms−2
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