WBJEE · Physics · Motion In One Dimension

A stone falls freely from rest and the total distance covered by it in the last second of its motion equals the distance covered by it in the first three seconds of its motion. The stone remains in the air for

A \(6 \mathrm{~s}\)
B \(5 \mathrm{~s}\)
C \(7 \mathrm{~s}\)
D \(4 \mathrm{~s}\)

Verified Solution

Answer & Solution

Correct Answer

(B) \(5 \mathrm{~s}\)

Step-by-step Solution

Detailed explanation

Hints : \(u=0\) \[ \begin{aligned} & \mathrm{S}_3=0+\frac{1}{2} g t^2=\frac{1}{2} \times 10 \times 9=45 \\ & \mathrm{~S}_t \text { th }=u+(2 t-1) \frac{g}{2} \\ & \mathrm{~S}_t \text { th }=0+5(2 t-1)=45 \\ & 2 t-1=9 \\ & t=5 \mathrm{sec} \end{aligned} \]

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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