TS EAMCET · Physics · Motion In One Dimension

A particle initially at rest is moving along a straight line with an acceleration of \(2 \mathrm{~ms}^{-2}\). At a time of 3 s after the beginning of motion, the direction of acceleration is reversed. The time from the beginning of the motion in which the particle returns to its initial position is

A \((3+\sqrt{3}) \mathrm{s}\)
B \((2+\sqrt{2}) \mathrm{s}\)
C \(3(2+\sqrt{2}) \mathrm{s}\)
D \(2(3+\sqrt{3}) \mathrm{s}\)

Verified Solution

Answer & Solution

Correct Answer

(C) \(3(2+\sqrt{2}) \mathrm{s}\)

Step-by-step Solution

Detailed explanation

Displacement at \(t=3 \mathrm{~s}\): \(s_1 = \frac{1}{2} a_1 t_1^2 = \frac{1}{2} (2)(3)^2 = 9 \mathrm{~m}\) Velocity at \(t=3 \mathrm{~s}\): \(v_1 = a_1 t_1 = (2)(3) = 6 \mathrm{~ms}^{-1}\) For total displacement \(S_{total} = 0\):…

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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