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  4. A car covers AB 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.

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Q. A car covers $AB$ 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 ______$ms ^{-1}$.Physics Question Image

JEE MainJEE Main 2022Motion in a Straight Line

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}} $
$=\frac{3}{\frac{1}{ V _{1}}+\frac{1}{ V _{2}}+\frac{1}{ V _{3}}}=\frac{1}{11}+\frac{1}{22}+\frac{1}{33}$
$=18 \,m / s$