First slide

Average Velocity

Question

A person travels along a straight road for the first half time with a velocity v₁, and the second half time with a velocity v₂. Then the mean velocity v is given by

Easy

A

$\bar{V} = \frac{V_{1} + V_{2}}{2}$
B

$\frac{2}{\bar{V}} = \frac{1}{V_{1}} + \frac{1}{V_{2}}$
C

$\bar{V} = \sqrt{V_{1} V_{2}}$
D

$\bar{V} = \sqrt{\frac{V_{2}}{V_{1}}}$

Solution

Let for the first half time f, the person travels a distance s₁. Hence
$v_{1} = \frac{S_{1}}{t} or S_{1} = V_{1} t$
For second half time, $V_{2} = \frac{S_{2}}{t} or S_{2} = V_{2} t$
$Now, V = \frac{Total displacement}{Total time} = \frac{s_{1} + s_{2}}{2 t}$
$= \frac{V_{1} t + V_{2} t}{2 t} = \frac{V_{1} + V_{2}}{2}$

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