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

Answer

C

Explanation

Distance travelled by police in t seconds = Vt
Distance travelled by theif = `x + 1/2ar^(2)`
`x+1/2a^(2)le Vt`
` implies (at^(2))/2+x-V_(t)=0`
`implies t= (V pm sqrt(v^(2)-2ax))/a`
For real value of t, `V^(2) ge 2ax`