A body initially at rest is moving with uniform acceleration a . Its velocity after n seconds is v .

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2.Motion in Straight Line

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

A

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

B

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

C

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

D

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

Solution

Here, $a=\frac{v-u}{t}=\frac{v-0}{n}=\frac{v}{n}$

Displacement in last $2\, s$

$\mathrm{S}_{\mathrm{n}}-\mathrm{S}_{\mathrm{n}-2}=\frac{1}{2} \mathrm{an}^{2}-\frac{1}{2} \mathrm{a}(\mathrm{n}-2)^{2}$

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

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

Standard 11

Physics

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