A particle is moving in one dimension (along \(\mathrm{x}\) axis) under the action of a variable force. It's initial position was \(16 \mathrm{~m}\) right of origin. The variation of its position ( \(\mathrm{x}\) ) with time ( \(\mathrm{t})\) is given as \(\mathrm{x}=-3 \mathrm{t}^3+18 \mathrm{t}^2+16 \mathrm{t}\), where \(\mathrm{x}\) is in \(\mathrm{m}\) and \(\mathrm{t}\) is in \(\mathrm{s}\). The velocity of the particle when its acceleration becomes zero is _______ \(\mathrm{m} / \mathrm{s}.\)

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.