Question

A police party is moving in a jeep at a constant
speed v. They saw a thief at a distance xon 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? [2011-E]​

Answer 1

answer : v² ≥ 2ax

explanation : given, speed of police party = v

distance between thief and police = x

acceleration of thief = a

let the police party catch the thief after time t sec.

so, distance covered by police party after time t, s = vt.

and distance covered by thief after time t, s'= 1/2 at²

to catch the thief,

s = x + s'

or, vt = x + 1/2at²

or, at² - 2vt + 2x = 0

or, t = {2v ± √{(2v)² - 4(a)(2x)}/2a

for the real value of t, (2v)² - 4(a)(2x) ≥ 0

or, 4v² - 8ax ≥ 0

or, v² ≥ 2ax

hence, answer is v² ≥ 2ax

Answer 2

Answer:

1. v^2 < 2ax

Explanation:

that is the answer