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Question

(D) Let the total distance be $2d$. The person travels distance $d$ with velocity $v_1$ and the remaining distance $d$ with velocity $v_2$. Time taken

Vedclass · Accepted Answer

$\frac{2v_1 v_2}{v_1 + v_2}$

Vedclass · Answer

(D) Let the total distance be $2d$. The person travels distance $d$ with velocity $v_1$ and the remaining distance $d$ with velocity $v_2$. Time taken for the first half is $t_1 = \frac{d}{v_1}$. Time taken for the second half is $t_2 = \frac{d}{v_2}$. Average velocity $v_{avg} = \frac{	ext{Total distance}}{	ext{Total time}} = \frac{2d}{t_1 + t_2}$. Substituting the values: $v_{avg} = \frac{2d}{\frac{d}{v_1} + \frac{d}{v_2}} = \frac{2d}{d(\frac{v_1 + v_2}{v_1 v_2})} = \frac{2v_1 v_2}{v_1 + v_2}$. Thus,the correct option is $D$.

$A$ person travels along a straight road for half the distance with velocity $v_1$ and the remaining half distance with velocity $v_2$. The average velocity is given by:

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