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Q.

A police party is chasing a dacoit in a jeep which is moving at a constant speed v. The dacoit is on a motor cycle. 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?

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a

v2≤ αx

b

v2≤2αx

c

v2≥2αx

d

v2 ≥ αx

answer is C.

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Detailed Solution

If police is able to catch the dacoit after time t, thenvt ≥ x+12αt2This gives α2t2-vt+x = 0or t= v±v2-2αxαFor t to be real, v2≥ 2αx

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A police party is chasing a dacoit in a jeep which is moving at a constant speed v. The dacoit is on a motor cycle. 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?