A person travels distance with velocity and then distance with velocity in the same direction. The average velocity of the person is , then the relation between , and will be: [2023]

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Q.
A person travels $x$ distance with velocity $v_{1}$ and then $x$ distance with velocity $v_{2}$ in the same direction. The average velocity of the person is $v$ , then the relation between $v$ , $v_{1}$ and $v_{2}$ will be: [2023]

Solution

Q.
A person travels $x$ distance with velocity $v_{1}$ and then $x$ distance with velocity $v_{2}$ in the same direction. The average velocity of the person is $v$ , then the relation between $v$ , $v_{1}$ and $v_{2}$ will be: [2023]

1 $v = v_{1} + v_{2}$

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

3 $\frac{2}{v} = \frac{1}{v_{1}} + \frac{1}{v_{2}}$

4 $\frac{1}{v} = \frac{1}{v_{1}} + \frac{1}{v_{2}}$

Ans.
(3)

$Average velocity = \frac{x + x}{\frac{x}{v_{1}} + \frac{x}{v_{2}}} = v$

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

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Solution

Q. A person travels x distance with velocity v1 and then x distance with velocity v2 in the same direction. The average velocity of the person is v, then the relation between v, v1 and v2 will be: [2023]

1 v=v1+v2

2 v=v1+v22

3 2v=1v1+1v2

4 1v=1v1+1v2

Ans. (3) Average velocity=x+xxv1+xv2=v 1v1+1v2=2v

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Q.
A person travels $x$ distance with velocity $v_{1}$ and then $x$ distance with velocity $v_{2}$ in the same direction. The average velocity of the person is $v$ , then the relation between $v$ , $v_{1}$ and $v_{2}$ will be: [2023]

1 $v = v_{1} + v_{2}$

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

3 $\frac{2}{v} = \frac{1}{v_{1}} + \frac{1}{v_{2}}$

4 $\frac{1}{v} = \frac{1}{v_{1}} + \frac{1}{v_{2}}$

Ans.
(3)

$Average velocity = \frac{x + x}{\frac{x}{v_{1}} + \frac{x}{v_{2}}} = v$

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