A car covers AB distance in three equal parts at... | Rectilinear Motion

JEE MAIN 2022

28-06-22 S2

Question

A car covers $A B$ distance with first one-third at velocity $\mathrm{v}_1 \mathrm{~ms}^{-1}$, second one-third at $\mathrm{v}_2 \mathrm{~ms}^{-1}$ and last onethird at $v_3 \mathrm{~ms}^{-1}$. If $v_3=3 v_1, v_2=2 v_1$ and $v_1=11 \mathrm{~ms}^{-1}$ then the average velocity of the car is $\mathrm{ms}^{-1}$

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Solution

$$ \left.\langle\overline{\mathrm{v}}\rangle=\frac{\text { Displacement }}{\text { time }} \right\rvert\, $$ (Let displacement be I) $$ \begin{aligned} & =\frac{\ell}{\left(\frac{\ell}{\mathrm{V}_3}+\frac{\ell}{\mathrm{V}_2}+\frac{\ell}{\mathrm{V}_1}\right) \frac{1}{3}}=\frac{3}{\frac{1}{\mathrm{~V}_1}+\frac{1}{\mathrm{~V}_2}+\frac{1}{\mathrm{~V}_3}}=\frac{3}{\frac{1}{11}+\frac{1}{22}+\frac{1}{33}} \\ & =18 \mathrm{~m} / \mathrm{s} \end{aligned} $$

Question Tags

JEE Main

Physics

Easy

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