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A Person Travelling on a Straight Line Moves with a Uniform Velocity V1 For a Distance Xand with a Uniform Velocity V2 For the Next Equal Distance. the Average Velocity V Is Given by - Physics

MCQ

A person travelling on a straight line moves with a uniform velocity v1 for a distance x and with a uniform velocity v2 for the next equal distance. The average velocity v is given by

Options

  • \[v = \frac{v_1 + v_2}{2}\]

  • \[v = \sqrt{v_1 v_2}\]

  • \[\frac{2}{v} = \frac{1}{v_1} + \frac{1}{v_2}\]

  • \[\frac{1}{v} = \frac{1}{v_1} + \frac{1}{v_2}\]

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Solution

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

Velocity is uniform in both cases; that is, acceleration is zero.

\[x = v_1 t_1 \Rightarrow t_1 = \frac{x}{v_1}\]

\[x = v_2 t_2 \Rightarrow t_2 = \frac{x}{v_2}\]

Total displacement, \[x' = 2x\]
Total time, \[t = t_1 + t_2\]
∴  Average velocity, \[v = \frac{x'}{t} = \frac{2 v_1 v_2}{v_1 + v_2}\]
\[\Rightarrow \frac{2}{v} = \frac{1}{v_1} + \frac{1}{v_2}\]

  Is there an error in this question or solution?
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APPEARS IN

HC Verma Class 11, 12 Concepts of Physics 1
Chapter 3 Rest and Motion: Kinematics
MCQ | Q 5 | Page 49
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