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  4. A bus travelling the first one-third distance at a speed of 10 km h-1, the next one-third at 20 km h-1 and last one third at 60 km h-1. The average speed of bus is

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Q. A bus travelling the first one-third distance at a speed of $10 \, km \, h^{-1}$, the next one-third at $20 \, km \, h^{-1}$ and last one third at $60 \, km \, h^{-1}$. The average speed of bus is

JIPMERJIPMER 2016Motion in a Straight Line

Solution:

Here $v_1=10\, km\, h ^{-1}$ for $1^{\text {st }} \frac{1}{3}{ }^{\text {rd }}$
distance $v_2=20 \,km\, h ^{-1}$ for $2^{\text {nd }} \frac{1}{3}^{\text {rd }}$
distance $v_3=60 \,km \,h ^{-1}$ for $3^{\text {rd }} \frac{1}{3}^{\text {rd }}$
distance $v_{\text {avg }}=\frac{3 v_1 v_2 v_3}{v_1 v_2+v_2 v_3+v_3 v_1}$
$=\frac{3 \times 10 \times 20 \times 60}{10 \times 20+20 \times 60+60 \times 10}$ $v_{a v g}=18 \,km \,h ^{-1}$