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

Options

A. `v^(2)leax`
B. `v^(2)le2ax`
C. `v^(2)ge2ax`
D. `v^(2)geax`

Answer

C

Explanation

If police is able to catch the dacoit after time t, then `vt=x+(1)/(2)alphat^(2)` this gives `(alpha)/(2)t^(2)-vt+x=0`
or `t=(v+-sqrt(v^(2)-2alphax))/(alpha)` for t be real `v^(2)gealphax`