Question

A police inspector in a jeep is chasing a pickpocket on a straight road.the jeep is going at its max speed 'v'(assumed uniform).the pickpocket rides on the motorcycle of a waiting friend when the jeep is at a distance'd' away and the motorcycle starts with acceleration'a' show that the pickpocket will be caught of (v greater than or equal to √2ad

Answer 1

The pickpocket will be caught after time t when they will be at the same coordinate.

Now,for the police inspector
s=vt

For the motorcycle
s'=1/2a*t^2

Now,also,since police inspector needs to cover d distance more than the motorcycle in the same time t

hence s = s'+d
vt=1/2a*t^2+d
at^2 -2vt+2d=0

hope it helps you.

Answer 2

Explanation:

v×t=x+1/2at^2

or, at^2-2vt+2x=0

or, 2v+√4v^2-4×2xa/2a

or, 2v-√4v^2-4×a/2a

4v^2-8xa greater than 0

4v^2 greater than 8xa

v^2 greater than 8xa/4

v^2 greater than 2xa

v greater than √2xa