First slide

Average Velocity

Question

A car completes its journey in a straight line in three equal parts with speeds $v_{1}, v_{2} and v_{3} respectivley . The average speed v is given by$

Easy

A

$\frac{v_{1} + v_{2} + v_{3}}{3}$
B

$3 \sqrt{v_{1} v_{2} v_{3}}$
C

$\frac{1}{v} = \frac{1}{v_{1}} + \frac{1}{v_{2}} + \frac{1}{v_{3}}$
D

$\frac{3}{v} = \frac{1}{v_{1}} + \frac{1}{v_{2}} + \frac{1}{v_{3}}$

Solution

Average speed, v = $\frac{Total distance}{Total time}$
= $\frac{s}{\frac{\frac{s}{3}}{v_{1}} + \frac{\frac{s}{3}}{v_{2}} + \frac{\frac{s}{3}}{v_{3}}} = \frac{3}{\frac{1}{v_{1}} + \frac{1}{v_{2}} + \frac{1}{v_{3}}}$
$\Rightarrow \frac{3}{v} = \frac{1}{v_{1}} + \frac{1}{v_{2}} + \frac{1}{v_{3}}$

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