Question

A body covers a total distance of 3s. The first s is covered with a velocity u the second s with V and the last s with omega. Then, the average velocity during the whole journey is

Answer 1

Answer:

Given:

Total distance = 3s

First part is covered with u , 2nd part with v , 3rd party with ω.

To find:

Average Velocity in the whole journey.

Concept:

Average Velocity is the ratio of total displacement to the total time taken.

Calculation:

$v_{avg} = \dfrac{total \: distance}{total \: time}$

$= > v_{avg} = \dfrac{3s}{ \dfrac{s}{u} + \dfrac{s}{v} + \dfrac{s}{ \omega} }$

$= > v_{avg} = \dfrac{3}{ \dfrac{1}{u} + \dfrac{1}{v} + \dfrac{1}{ \omega} }$

$= > v_{avg} = \dfrac{3}{ \bigg( \dfrac{uv + u \omega + v \omega}{uv \omega} \bigg) }$

$= > v_{avg} = \dfrac{3uv \omega}{ \bigg(uv + v \omega + u \omega \bigg)}$

So final answer :

$\boxed{ \sf{ \red{ \large{ v_{avg} = \dfrac{3uv \omega}{ \bigg(uv + v \omega + u \omega \bigg)}}}}}$

Answer 2

$\underline{ \huge \boxed{ \bold{ \mathfrak{ \purple{Answer}}}}}$

Given :

A body covers a total distance of 3s. The first s is covered with a velocity u the second s with v and the last s with $\omega$.

To Find :

Average velocity during the whole journey.

Formula :

$\: \: \: \dag \: \: \underline{ \boxed{ \bold{ \rm{ \pink{v_{av} = \frac{total \: distance}{total \: time}}}}}} \: \: \dag$

Calculation :

$\implies \rm \: v_{av} = \frac{3s}{ \frac{s}{u} + \frac{s}{v} + \frac{s}{ \omega} } \: \: \: ( \because{t} = \frac{distance}{velocity}) \\ \\ \therefore \rm \: v_{av} = \frac{3s}{s( \frac{1}{u} + \frac{1}{v} + \frac{1}{ \omega} )} \\ \\ \therefore \rm \: v_{av} = \frac{3}{ \frac{uv + v \omega + u \omega}{uv \omega} } \\ \\ \therefore \: \underline{ \boxed{ \bold{ \rm{ \orange{v{ \tiny{av}} = \frac{3uv \omega}{uv + v \omega + u \omega}}}}}} \: \: \purple{ \clubsuit}$

Short - trick :

let body covers 1/3 of total distance with velocity V1 another 1/3 distance with velocity V2 and final 1/3 distance with velocity V3 then average velocity is given by...

$\: \: \: \: \dag \: \underline{ \boxed{ \bold{ \rm{ \blue{v{ \tiny{av}} \orange= \frac \red{3v{ \tiny{1}}v{ \tiny{2}}v{ \tiny{3}}} \green{v{ \tiny{1}}v{ \tiny{2}} + v{ \tiny{2}}v{ \tiny{3}} + v{ \tiny{1}}v{ \tiny{3}}} }}}}} \: \dag$