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A policeparty is chasing a dacoit in a jeep which is moving at a constant speed v. The dacoit is on a motorcycle. When he is at a distance x from the jeep, he accelerates from rest at a constant rate α. Which of the following relations is true if the police is able to catch the dacoit?

a
v2 ≤ ax
b
v2 ≤ 2ax
c
v2 ³ 2ax
d
v2 ³ ax

detailed solution

Correct option is C

If police is able to catch the dacoit after time t, then vt=x+12αt2. This gives α2t2−vt+x=0⇒t=v±v2−2αxα. For t to be real, v2>2ax.

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