Solved: PHYSICS Question for NEET

NEET PHYSICSMedium

A person travelling in a straight line moves with a constant velocity v₁ for a certain distance x and with a constant velocity v₂ for the next equal distance. The average velocity v is given by the relation:

1/v = 1/v₁ + 1/v₂

2/v = 1/v₁ + 1/v₂

v/2 = (v₁ + v₂)/2

v = √v₁v₂

Step-by-Step Solution

Definition of Average Velocity: Average velocity is defined as the total displacement divided by the total time interval . $v_{avg} = \frac{\text{Total Displacement}}{\text{Total Time}}$
Calculate Time Intervals: For the first half distance $x$ , velocity is $v_1$ . Time taken $t_1 = \frac{x}{v_1}$ . For the second half distance $x$ , velocity is $v_2$ . Time taken $t_2 = \frac{x}{v_2}$ .
Calculate Total Values: Total Displacement $= x + x = 2x$ . Total Time $= t_1 + t_2 = \frac{x}{v_1} + \frac{x}{v_2} = x \left( \frac{1}{v_1} + \frac{1}{v_2} \right)$ .
Derive Relation: $v = \frac{2x}{x(\frac{1}{v_1} + \frac{1}{v_2})}$ $v = \frac{2}{\frac{1}{v_1} + \frac{1}{v_2}}$ Rearranging the terms: $\frac{1}{v} = \frac{\frac{1}{v_1} + \frac{1}{v_2}}{2}$ $\frac{2}{v} = \frac{1}{v_1} + \frac{1}{v_2}$

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