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Q.
If a school bus, on it's way to school, covers half the distance with velocity $v_1$ and other half with velocity $v_2$. The average velocity of the school bus would be:
Kinematics
Solution:
Time taken for first half of the distance $=t_1$ $=\frac{d}{v_1}$
Time taken for second half of the distance $=t_2=\frac{d}{v_2}$
$\text { Hence, } $
$V_{\text {average }} =(\frac{\text { Total distance }}{\text { Total time }}) $
$ =(\frac{d+d}{t_1+t_2}) $
$ =\frac{2 d}{(\frac{d}{v_1})+(\frac{d}{v_2})} $
$ =\frac{2}{(\frac{1}{v_1})+(\frac{1}{v_2})} $
$ =\frac{2 v_1 v_2}{v_1+v_2} $
$ \therefore v_{\text {average }}=\frac{2 v_1 v_2}{v_1+v_2}$