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 ax`
B. `v^(2) lt 2ax`
C. `v^(2) ge 2ax`
D. `v^(2) = ax`

Answer

(c )

Explanation

Let the police catch the thief after time t
Then, `S_("Police"): = vt` and `S_"Thief" = 1/2 at^(2)`
The police will catch the thief,
`x + 1/2 at^(2) = vt`
`1/2 at^(2) - vt + x = 0`
`t= (v+- sqrt(v^(2)-2ax))/(a)`
`v^(2)-2ax ge0` or `v^(2) ge 2ax`