A person travels x distance with velocity v1 and then x distance with velocity v2 in the same direction. The average vel

Question

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:

Accepted Answer

Given: A person travels equal distances $x$ and $x$ with velocities $v_1$ and $v_2$ respectively in the same direction.

Find: The relation between average velocity $v$ , $v_1$ , and $v_2$ .

For the first part of the journey, time taken is

t_1 = \frac{x}{v_1}

For the second part of the journey, time taken is

t_2 = \frac{x}{v_2}

Total displacement is

2x

and total time is

t_1 + t_2 = \frac{x}{v_1} + \frac{x}{v_2} = x\left(\frac{1}{v_1} + \frac{1}{v_2}\right)

Average velocity is

v = \frac{\text{Total displacement}}{\text{Total time}} = \frac{2x}{x\left(\frac{1}{v_1} + \frac{1}{v_2}\right)} = \frac{2}{\left(\frac{1}{v_1} + \frac{1}{v_2}\right)}

Therefore,

\frac{2}{v} = \frac{1}{v_1} + \frac{1}{v_2}

So, the correct option is C. The solution labels the option as D, but the derived relation clearly matches option C in the given options.

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