Question

A person completes half of its his journey with speed $v _ { 2 }$. The average speed of the person is

• A. $v = \frac { v _ { 1 } + v _ { 2 } } { 2 }$
• B. $v = \frac { 2 v _ { 1 } v _ { 2 } } { v _ { 1 } + v _ { 2 } }$
• C. $v = \frac { v _ { 1 } v _ { 2 } } { v _ { 1 } + v _ { 2 } }$
• D. $v = \sqrt { v _ { 1 } v _ { 2 } }$

Answer 1

Answer: (B)

$v = \frac { 2 v _ { 1 } v _ { 2 } } { v _ { 1 } + v _ { 2 } }$

Answer 2

In this problem total distance is divided into two equal parts. So

$\frac { \frac { d } { 2 } + \frac { d } { 2 } } { \frac { d / 2 } { v _ { 1 } } + \frac { d / 2 } { v _ { 2 } } }$

⇒ $\frac { 2 v _ { 1 } v _ { 2 } } { v _ { 1 } + v _ { 2 } }$