A person travelled the first half of the journey with a velocity of $ 20 \mathrm{~m} / \mathrm{s} $ and the rest with a velocity of $ 30 \mathrm{~m} / \mathrm{s} $. Find the average velocity of the whole journey.

Given:

Velocity in the first half of the journey, $V_1$= 20 m/s

Velocity in the rest of the journey, $V_2$ = 30 m/s

To find: Average Velocity, $V_{av}$

Solution:

Let $s$ = displacement of half of the journey

We know that-

$Average\ Velocity=\frac {Total\ displacemnt}{Total\ time}$

So, we have to find out total displacement and total time.

Now, 

We know that-

$Time=\frac {Displacemnt}{Velocity}$

Therefore,

Time taken in first half of the journey = $\frac {s}{20}$

Time taken in rest of the journey = $\frac {s}{30}$

$Total\ time\ taken=Time\ taken\ in\ first\ half\ of\ the\ journey\ + Time\ taken\ in\ rest\ of\ the\ journey$

$Total\ time\ taken=\frac {s}{20}+\frac {s}{30}$

$Total\ time\ taken=\frac {3s+2s}{60}$

$Total\ time\ taken=\frac {5s}{60}$

$Total\ time\ taken=\frac {s}{12}$

Now, putting the value of total time and total displacement in the average velocity formula we get-

$Average\ Velocity=\frac {s+s}{\frac {s}{12}}$

$V_{av}=\frac {2s}{\frac {s}{12}}$

$V_{av}=\frac {2s\times {12}}{s}$

$V_{av}=\frac {24s}{s}$

 $V_{av}=24m/s$

Thus, the average velocity  $V_{av}$ of the whole journey will be 24m/s.

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Updated on: 10-Oct-2022

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