A body moves in a straight line with speeds v | vedclass

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Question

(C) Given that the distances travelled by the body are in the ratio $1: 2$.Let the distance travelled with speed $v_1$ be $s$. Then, the distance trav

Vedclass · Accepted Answer

$\frac{3 v_1 v_2}{v_2+2 v_1}$

Vedclass · Answer

(C) Given that the distances travelled by the body are in the ratio $1: 2$.Let the distance travelled with speed $v_1$ be $s$. Then, the distance travelled with speed $v_2$ will be $2s$.Average speed is defined as the total distance travelled divided by the total time taken.Total distance = $s + 2s = 3s$.Time taken for the first part, $t_1 = \frac{s}{v_1}$.Time taken for the second part, $t_2 = \frac{2s}{v_2}$.Total time taken, $T = t_1 + t_2 = \frac{s}{v_1} + \frac{2s}{v_2} = s \left( \frac{1}{v_1} + \frac{2}{v_2} ight) = s \left( \frac{v_2 + 2v_1}{v_1 v_2} ight)$.Average speed, $v_{	ext{avg}} = \frac{	ext{Total distance}}{	ext{Total time}} = \frac{3s}{s \left( \frac{v_2 + 2v_1}{v_1 v_2} ight)} = \frac{3 v_1 v_2}{v_2 + 2v_1}$.

$A$ body moves in a straight line with speeds $v_1$ and $v_2$ for distances which are in the ratio $1: 2$. Find the average speed.

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