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) le alpha x`
B. `v^(2) le2alpha x`
C. `v^(2)le 2alpha x`
D. `v^(2) le alpha x`

Answer

C

Explanation

If police is able to catch the dacoit aftre tive `t` then
`vt=x +(1)/(2) alpha t^(2)` his gives `(alpha)/(2) 1^(2) -vt+ x=0`
or `t=(v +- sqrt(v^(2) -2 alpha x))/(alpha)` For `t` to be real, `v^(2) le 2ax`.