TS EAMCET · Physics · Motion In One Dimension

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?

A \(v^2 < a x\)
B \(v^2 < 2 a x\)
C \(v^2 \geq 2 a x\)
D \(v^2=a x\)

Verified Solution

Answer & Solution

Correct Answer

(C) \(v^2 \geq 2 a x\)

Step-by-step Solution

Detailed explanation

Let the police party catch the thief after \(t\) second. \(\therefore\) Distance travelled by police party in \(t\) second \(=v t\) and distance travelled by thief \(=x+\frac{1}{2} \alpha t^2\) So, \(\quad x+\frac{1}{2} \alpha t^2 \leq v t\) or…

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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