First slide

Average Velocity

Question

A person travelling in a straight line moves with a constant velocity v₁ for certain distance x and with a constant velocity v₂ for next equal distance. The average velocity v is given by the relation [NEET 2019]

Moderate

A

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

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

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

$v = \sqrt{v_{1} v_{2}}$

Solution

For distance x, the person moves with constant velocity v₁and for another x distance, he moves with constant velocity of v₂ then
Total distance travelled by the person,
D = x + x = 2x
Total time taken to cover that distance,
, $T = t_{1} + t_{2} = \frac{x}{v_{1}} + \frac{x}{v_{2}} (∵ t = \frac{Distance}{Velocity})$
Average velocity,
   $v_{av} = \frac{Total distance}{Total time} = \frac{D}{T}$
   $v = \frac{2 x}{\frac{x}{v_{1}} + \frac{x}{v_{2}}} = \frac{2}{\frac{1}{v_{1}} + \frac{1}{v_{2}}} (∵ v_{av} = v)$
$\Rightarrow$    $\frac{2}{v} = \frac{1}{v_{1}} + \frac{1}{v_{2}}$

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