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Concepts Of Physics MCQ Edition [Volume 1]

Exam: Concepts Of Physics MCQ Edition [Volume 1]
Subject: Physics
Chapter: Rest and Motion Kinematics

Concepts Of Physics MCQ Edition [Volume 1] · Physics · Rest and Motion Kinematics

A person moving along a straight line travels with a uniform...

A person moving along a straight line travels with a uniform velocity

v_1

for a distance

x

, and then with a uniform velocity

v_2

for the next equal distance. The average velocity

v

is given by

Options

A $\dfrac{2}{v} = \dfrac{1}{v_1} + \dfrac{1}{v_2}$
B $\dfrac{1}{v} = \dfrac{1}{v_1} + \dfrac{1}{v_2}$
C $v = \dfrac{v_1 + v_2}{2}$
D $v = \sqrt{v_1 v_2}$

Correct answer

A. $\dfrac{2}{v} = \dfrac{1}{v_1} + \dfrac{1}{v_2}$

Step-by-step solution

Time taken to travel the first distance

x

is

t_1 = \dfrac{x}{v_1}

Time taken to travel the next distance

x

is

t_2 = \dfrac{x}{v_2}

Total distance traveled is

x + x = 2x

Total time taken is

t = t_1 + t_2 = \dfrac{x}{v_1} + \dfrac{x}{v_2}

Average velocity

v = \dfrac{\text{Total distance}}{\text{Total time}} = \dfrac{2x}{\dfrac{x}{v_1} + \dfrac{x}{v_2}}

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

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

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