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Question

(C) Given that the body starts from rest,the initial velocity $u = 0$. Let the uniform acceleration be $a$.At time $t = n$,the velocity $v = u + at =

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$\frac{2v(n-1)}{n}$

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(C) Given that the body starts from rest,the initial velocity $u = 0$. Let the uniform acceleration be $a$.At time $t = n$,the velocity $v = u + at = 0 + an$,so $a = \frac{v}{n}$.The displacement in the $k^{	ext{th}}$ second is given by $S_k = u + \frac{a}{2}(2k - 1)$.Since $u = 0$,$S_k = \frac{a}{2}(2k - 1)$.The displacement in the $n^{	ext{th}}$ second is $S_n = \frac{a}{2}(2n - 1)$.The displacement in the $(n-1)^{	ext{th}}$ second is $S_{n-1} = \frac{a}{2}(2(n-1) - 1) = \frac{a}{2}(2n - 3)$.The total displacement in these two seconds is $S_{total} = S_n + S_{n-1} = \frac{a}{2}(2n - 1 + 2n - 3) = \frac{a}{2}(4n - 4) = 2a(n - 1)$.Substituting $a = \frac{v}{n}$,we get $S_{total} = 2(\frac{v}{n})(n - 1) = \frac{2v(n - 1)}{n}$.

$A$ body starts from rest with uniform acceleration and its velocity at a time of $n$ seconds is $v$. The total displacement of the body in the $n^{\text{th}}$ and $(n-1)^{\text{th}}$ seconds of its motion is:

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