First slide

Average velocity

Question

A passenger travels along the straight road for half the distance with velocity v₁, and the remaining half distance with velocity v₂. Then average velocity is given by

Moderate

A

v₁ v₂
B

$v_{2}^{2} / v_{1}^{2}$
C

$(v_{1} + v_{2}) / 2$
D

$2 v_{1} v_{2} / (v_{1} + v_{2})$

Solution

$\frac{\frac{X}{2} + \frac{X}{2}}{\frac{X}{2 v_{1}} + \frac{X}{2 v_{2}}} = \frac{1}{(\frac{v_{2} + v_{1}}{2 v_{1} v_{2}})} = \frac{2 v_{1} v_{2}}{v_{1} + v_{2}}$

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