Question

A man covers half of his distance with velocity 10m/s and remaining with 20m/s.what is the average velocity

Answer 1

$\color{darkblue}\underline{\underline{\sf Given-}}$

• Man covers half Distance with velocity ${\sf (v_1)=10m/s}$
• And other half Distance with velocity ${\sf (v_2)=20m/s}$

$\color{darkblue}\underline{\underline{\sf To \: Find-}}$

• Average Velocity ${\sf v_{av}}$.

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$\color{darkblue}\underline{\underline{\sf Formula \: Used-}}$

$\color{violet}\bullet\underline{\boxed{\sf V_{av}=\dfrac{Displacement}{Time}}}$

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$\implies{\sf v_{av}=\dfrac{2s}{\dfrac{s}{10}+\dfrac{s}{20}}}$

$\implies{\sf v_{av}=\dfrac{2s}{\dfrac{20s+10s}{10×20}} }$

$\implies{\sf v_{av}=2s×\dfrac{200}{30s} }$

$\color{red}\implies{\sf v_{av}=\dfrac{40}{3}m/s }$

$\color{darkblue}\underline{\underline{\sf Answer-}}$

Average Velocity of man is $\color{red}{\sf \dfrac{40}{3}}$.

Answer 2

Solution :

⏭ Given:

✏ A man covered first half of total distance with velocity 10mps and second half of total distance with velocity 20mps.

⏭ To Find:

✏ Average velocity during entire journey.

⏭ Formula:

✏ If body coveres first half of total distance with velocity V1 and second half of total distance with velocity V2, then average velocity is given by

$\star \: \boxed{ \tt{ \pink{V_{av} = \dfrac{2V_1V_2}{V_1 + V_2}}}}$

⏭ Calculation:

$\dashrightarrow \sf \: V_{av} = \dfrac{2 \times 10 \times 20}{10 + 20} \\ \\ \dashrightarrow \sf \: V_{av} = \dfrac{400}{30} \\ \\ \dashrightarrow \boxed{\tt{ \orange{ \large{ V_{av} = 13.33 \: mps}}}}$

⏭ Additional information:

• Average velocity is defined as ratio of total distance covered to the total time taken.
• It is vector quantity.