Question

A Vehicle starts at A with a speed of 20 km/hr and reaches B. then the vehicle returns to starting point A on the same path with a speed of 80 km/hr. What is the average speed.

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Answer 1

Average speed

$\implies\rm V_{av} = \dfrac{ Total\: distance}{Total\: time}$

Distance : Actual path travelled by object.

Solution:

$\implies\rm V_{av} = \dfrac{ AB+BA}{t_1 + t_2}$

$\implies\rm V_{av} = \dfrac{ x + x}{\dfrac{x}{v_1} + \dfrac{x}{v_2}}$

$\implies\rm V_{av} = \dfrac{ 2x}{\dfrac{x}{v_1} + \dfrac{x}{v_2}}$

$\implies\rm V_{av} = \dfrac{ 2}{\dfrac{1}{v_1} + \dfrac{1}{v_2}}$

$\implies\rm V_{av} = \dfrac{2}{\dfrac{v_1 +v_2}{v_1v_2}}$

$\implies\rm V_{av} = \dfrac{2v_1v_2}{v_1 +v_2}$

$\implies\rm V_{av} = \dfrac{2\times 20\times 80}{20+80 }$

$\implies\rm V_{av} = \dfrac{3200}{100}$

$\implies\bf V_{av} = 32\: kmh^{-1}$

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Answer 2

Explanation:

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$\large\bf{\underline{\red{VERIFIED✔}}}$

Average speed

$\implies\rm V_{av} = \dfrac{ Total\: distance}{Total\: time}$

Distance : Actual path travelled by object.

Solution:

$\implies\rm V_{av} = \dfrac{ AB+BA}{t_1 + t_2}$

$\implies\rm V_{av} = \dfrac{ x + x}{\dfrac{x}{v_1} + \dfrac{x}{v_2}}$

$\implies\rm V_{av} = \dfrac{ 2x}{\dfrac{x}{v_1} + \dfrac{x}{v_2}}$

$\implies\rm V_{av} = \dfrac{ 2}{\dfrac{1}{v_1} + \dfrac{1}{v_2}}$

$\implies\rm V_{av} = \dfrac{2}{\dfrac{v_1 +v_2}{v_1v_2}}$

$\implies\rm V_{av} = \dfrac{2v_1v_2}{v_1 +v_2}$

$\implies\rm V_{av} = \dfrac{2\times 20\times 80}{20+80 }$

$\implies\rm V_{av} = \dfrac{3200}{100}$

$\implies\bf V_{av} = 32\: kmh^{-1}$

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