If a person moving along a straight line path covers first half distance with velocity ' $\mathrm{V}_1$ '…
If a person moving along a straight line path covers first half distance with velocity ' $\mathrm{V}_1$ ' and the next half distance with velocity ' $\mathrm{V}_2$ ', then the average velocity of the person is
$\frac{V_1+V_2}{2}$
$\frac{\left(V_1+V_2\right)}{2 \sqrt{V_1 V_2}}$
$\frac{2}{\frac{1}{V_1}+\frac{1}{V_2}}$
$\frac{V_1 V_2}{V_1+V_2}$
Solution
Time taken for the first half distance is
$t_1=\frac{d}{2 v_1}$
Time taken for the second half distance is
$t_2=\frac{d}{2 v_2}$
Average velocity $=\frac{\text { Total distance }}{\text { Total time }}$
$\begin{aligned} & =\frac{d}{t_1+t_2}=\frac{d}{\frac{d}{2 v_1}+\frac{d}{2 v_2}} \\ & =\frac{1}{\frac{v_1+v_2}{2 v_1 v_2}}=\frac{2 v_1 v_2}{v_1+v_2}\end{aligned}$