A body starts from rest with uniform acceleration. If its velocity after n second is (\nu,) then its displacement in the last two seconds is
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\(\boxed{} \quad v = 0 + na \Rightarrow a = v/n\)
Now, distance travelled in n sec . ⇒ ⇒ \(S_{n} = \frac{1}{2} an^{2}\) and distance travelled in \(\left(n - 2\right) \sec\) ⇒ ⇒ \(S_{n-2} = \frac{1}{2} a (n-2)^2\)
∴ ∴ Distance travelled in last two seconds,
= S_{n} - S_{n-2} \(= \frac{1}{2} a n^{2} - \frac{1}{2} a (n - 2)^{2}\)
\(= \frac{a}{2} \left[ n^{2} - (n-2)^{2} \right]\) \(= \frac{a}{2} [n + (n - 2)][n - (n - 2)]\)
= a(2n - 2) \(\frac{V}{n} = -(2n - 2)\) \(= \frac{2v(n-1)}{n}\)
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