A body starts from rest with uniform acceleration a, its velocity after n,seconds is v . disp

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2.Motion in Straight Line

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A body starts from rest with uniform acceleration $a,$ its velocity after $n\,seconds$ is $v$. The displacement of the body in last $3\,s$ is : (assume total time of journey from $0$ to $n\,seconds$ )

A

$\frac{{v(6n - 9)}}{{2n}}$

B

$\frac{2{v(6n - 9)}}{{n}}$

C

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

D

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

Solution

$\mathrm{Sn}=\frac{1}{2} \mathrm{an}^{2}$

$S_{n-3}=\frac{1}{2} a(n-3)^{2} \quad$ Also $V=a n \Rightarrow a=V / n$

So, $S_{n}-S_{n-3}=\frac{1}{2} \cdot \frac{V}{n} \quad n^{2}-(n-3)^{2}$

Displacement in last $3$ second $=\frac{(6 n-9) \mathrm{V}}{2 \mathrm{n}}$

Standard 11

Physics

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