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  • A person travels x distance with velocity  and then x distance with velocity <img alt="v_{2}" src="https://en

A person travels x distance with velocity v_{1} and then x distance with velocity v_{2}  in the same direction. The average velocity of the person is v, then the relation between v,\; v_{1} and v_{2} will be.

Option: 1

\mathrm{v}=\mathrm{v}_1+\mathrm{v}_2


Option: 2

\frac{1}{\mathrm{v}}=\frac{1}{\mathrm{v}_1}+\frac{1}{\mathrm{v}_2}


Option: 3

\frac{2}{\mathrm{v}}=\frac{1}{\mathrm{v}_1}+\frac{1}{\mathrm{v}_2}


Option: 4

\mathrm{v}=\frac{\mathrm{v}_1+\mathrm{v}_2}{2}


Answers (1)

best_answer

Time taken b/w \mathrm{A} \& \mathrm{~B} \Rightarrow \mathrm{t}_1=\frac{x}{v_1}

Time between b/w B \& C \Rightarrow t_2=\frac{x}{v_2}

\text { Average velocity }(v)=\frac{\text { Total displacement }}{\text { Total time }}=\frac{x+x}{t_1+t_2}=\frac{2 x}{\frac{x}{v_1}+\frac{x}{v_2}}

(v)=\frac{2 v_1 v_2}{v_1+v_2}                 Or                 \frac{2}{\mathrm{v}}=\frac{1}{\mathrm{v}_1}+\frac{1}{\mathrm{v}_2}

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Sayak

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