A car covers A B distance with first one-third at velocity v _{1} ms ^{-1} , second one-third at v _

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2.Motion in Straight Line

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A car covers $A B$ distance with first one-third at velocity $v _{1} ms ^{-1}$, second one-third at $v _{2} ms ^{-1}$ and last one-third at $v _{3} ms ^{-1}$. If $v _{3}=3 v _{1}, v _{2}=2 v _{1}$ and $v _{1}=11\,ms ^{-1}$ then the average velocity of the car is________ $ms ^{-1} .$

A

$17$

B

$16$

C

$20$

D

$18$

(JEE MAIN-2022)

Solution

$\langle\overrightarrow{ v }\rangle=\frac{\text { Displacement }}{\text { time }}$

(Let displacement be $l$ )

$=\frac{\ell}{\left(\frac{\ell}{ V _{3}}+\frac{\ell}{ V _{2}}+\frac{\ell}{ V _{1}}\right) \frac{1}{3}}$

$=\frac{3}{\frac{1}{ V _{1}}+\frac{1}{ V _{2}}+\frac{1}{ V _{3}}}=\frac{3}{\frac{1}{11}+\frac{1}{22}+\frac{1}{33}}$

$=18\,m / s$

Standard 11

Physics

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(JEE MAIN-2023)