A police party is moving in a jeep at a constant speed v. They saw a thief at a distance x on a motorcycle which is at rest. The moment the police saw the thief, the thief started at constant acceleration a. Which of the following relations is true if the police is able to catch the thief?

Options

A. `v^2 le alpha x`
B. `v^2 le 2 alpha x`
C. `v^2 ge 2 alpha x`
D. `v^2 ge alpha x`

Answer

C

Explanation

If police is able to catch the dacoit after time `t`, then
`vt ge x + (1)/(2) alpha t^2`
This gives `(alpha)/(2) t^2 - vt + x = 0`
or `t = (v+- sqrt(v^2 - 2 alpha x))/(alpha)`
For `t` to be real, `v^2 ge 2 alpha x`.