COMEDK · Physics · 3. Motion In One Dimension

The nucleus of a helium atom travels along the inside of a straight hollow tube \(4 \mathrm{~m}\) long which forms part of a particle accelerator. If one assumes uniform acceleration, how long is the particle in the tube if it enters at a speed of \(2000 \mathrm{~m} / \mathrm{s}\) and leaves at \(8000 \mathrm{~m} / \mathrm{s}\)

A \(3.3 \times 10^{-4} \mathrm{~s}\)
B \(0.6 \times 10^{-4}\) s
C \(4 \times 10^{-4} \mathrm{~s}\)
D \(8 \times 10^{-4} \mathrm{~s}\)

Verified Solution

Answer & Solution

Correct Answer

(D) \(8 \times 10^{-4} \mathrm{~s}\)

Step-by-step Solution

Detailed explanation

Given the length of the tube \(s = 4 \text{ m}\), the initial velocity \(u = 2000 \text{ m/s}\), and the final velocity \(v = 8000 \text{ m/s}\). Assuming uniform acceleration, the average velocity \(v_{avg}\) is given by the formula \(v_{avg} = \dfrac{u + v}{2}\). Substituting…

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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