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Question

(D) Given that the body starts from rest,initial velocity $u = 0$.Let the uniform acceleration be $a$.After $n$ seconds,the velocity is $\upsilon = u

Vedclass · Accepted Answer

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

Vedclass · Answer

(D) Given that the body starts from rest,initial velocity $u = 0$.Let the uniform acceleration be $a$.After $n$ seconds,the velocity is $\upsilon = u + an = 0 + an$,so $a = \frac{\upsilon}{n}$.The displacement in $n$ seconds is $S_n = \frac{1}{2}an^2$.The displacement in $(n - 2)$ seconds is $S_{n-2} = \frac{1}{2}a(n - 2)^2$.The displacement in the last two seconds is $\Delta S = S_n - S_{n-2}$.$\Delta S = \frac{1}{2}an^2 - \frac{1}{2}a(n - 2)^2 = \frac{a}{2}[n^2 - (n - 2)^2]$.Using the identity $x^2 - y^2 = (x - y)(x + y)$:$\Delta S = \frac{a}{2}[n - (n - 2)][n + (n - 2)] = \frac{a}{2}[2][2n - 2] = a(2n - 2)$.Substituting $a = \frac{\upsilon}{n}$:$\Delta S = \frac{\upsilon}{n}(2n - 2) = \frac{2\upsilon(n - 1)}{n}$.

$A$ body starts from rest with uniform acceleration. If its velocity after $n$ seconds is $\upsilon$,then its displacement in the last two seconds is

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