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

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`.