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A person travelling along a straight Road for half the distance with the velocity V1 and the remaining half distance with velocity V2 the average velocity is given by

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Let body covers first d/2 distance in time t1 and the remaining d/2 distance in time t2

Total distance covered by body = d

\begin{array}{l} \mathrm{V}_{\mathrm{av}}=\frac{\mathrm{d}}{\mathrm{t}_{1}+\mathrm{t}_{2}} \\\\ \mathrm{V}_{\mathrm{av}}=\frac{\mathrm{d}}{\frac{\mathrm{d}}{2 \mathrm{v}_{1}}+\frac{\mathrm{d}}{2 \mathrm{v}_{2}}}=\frac{\mathrm{d}}{\mathrm{d}\left(\frac{\mathrm{v}_{1}+\mathrm{v}_{2}}{2 \mathrm{V}_{1} \mathrm{V}_{2}}\right)} \\\\ \mathrm{V}_{\mathrm{av}}=\frac{2 \mathrm{V}_{1} \mathrm{V}_{2}}{\mathrm{V}_{1}+\mathrm{V}_{2}} \end{array}

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avinash.dongre

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