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# A body travels first half a distance with velocity v$_0$. The remaining distance was covered with velocity v$_1$ for half the time and v$_2$ for the remaining time. Find the average velocity over the whole time of motion?

Answer: $\large\frac{2v_0 (v_1+v_2)}{2v_0+v_1+v_2}$
Average velocity $\overline{v} = \large\frac{2 v1 v2}{v1+v2}$
In this case, a body travels first half a distance with velocity $v_0 \rightarrow v1 = v_0$.
For the 2nd half, average velocity $v2 = \large\frac{1}{2}$$( v_1+v_2)$
$\Rightarrow \overline{v} = \large\frac{2 v_0 \frac{v_1+v_2}{2}}{v_0 + \frac{v_1+v_2}{2}}$
$\Rightarrow \overline{v} = \large\frac{2v_0 (v_1+v_2)}{2v_0+v_1+v_2}$