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(A) Given that the body starts from rest,initial velocity $u = 0$. After $n$ seconds,the velocity is $v$. Using the first equation of motion,$v = u +

Vedclass · Accepted Answer

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

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(A) Given that the body starts from rest,initial velocity $u = 0$. After $n$ seconds,the velocity is $v$. Using the first equation of motion,$v = u + an$,we get $v = 0 + an$,which implies $a = \frac{v}{n}$. The displacement in the last $2 \ s$ is the difference between the total displacement in $n$ seconds and the displacement in $(n - 2)$ seconds. $S_{last 2s} = S_n - S_{n-2} = \frac{1}{2}an^2 - \frac{1}{2}a(n-2)^2$. $S_{last 2s} = \frac{1}{2}a [n^2 - (n^2 - 4n + 4)] = \frac{1}{2}a [4n - 4] = 2a(n - 1)$. Substituting $a = \frac{v}{n}$,we get $S_{last 2s} = 2(\frac{v}{n})(n - 1) = \frac{2v(n - 1)}{n}$.

$A$ body initially at rest is moving with uniform acceleration $a$. Its velocity after $n$ seconds is $v$. The displacement of the body in the last $2 \ s$ is

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