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) lt alpha X`
B. `V^(2) lt 2alpha X`
C. `V^(2) gt 2alphaX`
D. `V^(2)=alphaX`

Answer

C

Explanation

Distance travelled by the police party in `t` sec is vt. Distance travelled by thief `x+(1)/(2)alphat^(2)`
`implies +(1)/(2)alphat^(2)le vt implies(alphat^(2))/(2)-vt+x=0`
`alphat^(2)-2vt+2x=0 implies t=2y+-sqrt(4v^(2)-8alphax)`
`4v^(2)gt8alphax,v^(2)gt2alphax`