A police party 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. Which of the following relations is true if the police is able to catch the dacoit?

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v2≤αx

v2≤2αx

v2≥2αx

v2≥αx

answer is C.

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Detailed Solution

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

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