Question

A person travels along a straight road for half
the distance with velocity V, and the remaining
half distance with velocity V2 average
velocity is given by
​

Answer 1

Answer:

the average velocity is given by V3 because average velocity is equal to total distance by total time taken so time is not given and the distance is V+V2 =V3

please make it as brain list Matt

Answer 2

$\red{\bigstar}\underline{\underline{\textsf{\textbf{ Given :- }}}}$

• A person travels along a straight road for half the distance with velocity v₁ and the remaining half distance with a velocity v₂ .

$\red{\bigstar}\underline{\underline{\textsf{\textbf{ To Find :- }}}}$

• The average velocity of the journey .

$\red{\bigstar}\underline{\underline{\textsf{\textbf{ Solution :- }}}}$

We need to find the average velocity of the journey .We know that average velocity is defined as the total displacement travelled by total time taken. Therefore let us take ,

• The person took a time of t₂ to travel second half and a time of t₁ to travel first half of the motion.

For the figure refer to the attachment . Now we know that , velocity is equal to displacement by time. So that ,

$\tt\dashrightarrow t_1 = \dfrac{ x}{v_1}\\\\\\\tt\dashrightarrow t_2 = \dfrac{x}{v_2}$

❒ So that ,

$\tt\dashrightarrow Avg . \ Velocity =\dfrac{ Total \ displacement\ travelled }{Total \ time\ taken } \\\\\\\tt\dashrightarrow v_{(avg)}= \dfrac{ x+x}{t_1+t_2} \\\\\\\tt\dashrightarrow v_{(avg)}= \dfrac{ 2x}{\dfrac{x}{v_1}+\dfrac{x}{v_2}} \\\\\\\tt\dashrightarrow v_{(avg)}= \dfrac{2x}{\dfrac{xv_1+xv_2}{v_1v_2}} \\\\\\\tt\dashrightarrow v_{(avg)}= \dfrac{(2x) * ( v_1v_2)}{x( v_1+v_2)} \\\\\\\tt\dashrightarrow \underset{\blue{\sf Required\ Answer}}{\underbrace{\boxed{\pink{\frak{Velocity_{(avg)}= \dfrac{ 2v_1v_2}{v_1+v_2}}}}}}$

$\rule{200}2$