MHT CET · Physics · Motion In One Dimension
A body starts from rest and moves with a uniform acceleration. The ratio of the distance covered by the body in the \(\mathrm{n}^{\text {th }}\) second of its motion to the total distance travelled in n second is
- A \(\frac{2}{n^2}-\frac{1}{n}\)
- B \(\frac{1}{n}-\frac{1}{n^2}\)
- C \(\frac{2}{n}-\frac{1}{n^2}\)
- D \(\frac{2}{n^2}+\frac{1}{n}\)
Answer & Solution
Correct Answer
(C) \(\frac{2}{n}-\frac{1}{n^2}\)
Step-by-step Solution
Detailed explanation
\(S_n = u + \frac{a}{2}(2n - 1) = 0 + \frac{a}{2}(2n - 1)\) \(S_{total} = ut + \frac{1}{2}at^2 = 0 \cdot n + \frac{1}{2}an^2 = \frac{1}{2}an^2\)
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