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Relative motion based problems

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


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, v22ax

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