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Explain Clearly, with Examples, the Distinction Between Magnitude of Average Velocity Over an Interval of Time, and the Average Speed Over the Same Interval - CBSE (Science) Class 11 - Physics

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Question

Explain clearly, with examples, the distinction between magnitude of average velocity over an interval of time, and the average speed over the same interval. [Average speed of a particle over an interval of time is defined as the total path length divided by the time interval]. Show in both (a) and (b) that the second quantity is either greater than or equal to the first.

When is the equality sign true? [For simplicity, consider one-dimensional motion only].

Solution 1

Magnitude of average velocity = `"Magnitude of displacement"/"Time interval"`

For the given particle.

Average velocity =  AC/t

Average speed = `"Total path length"/ "Time interval"`

`=(AB+BC)/t`

Since (AB + BC) > AC, average speed is greater than the magnitude of average velocity. The two quantities will be equal if the particle continues to move along a straight line.

Solution 2

Suppose, in the above example, the particle takes time t to cover the whole journey. Then, the magnitude of the average velocity of the particle over time-interval t is = Magnitude of displacement /Time-interval =0/t =0

While the average speed of the particle over the same time-interval is =Total path length /Time-interval= 2 AB /t

Again, the second quantity (average speed) is greater than the first (magnitude of average velocity).

  Is there an error in this question or solution?

APPEARS IN

 NCERT Solution for Physics Textbook for Class 11 (2018 to Current)
Chapter 3: Motion in a Straight Line
Q: 13.2 | Page no. 57

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Solution Explain Clearly, with Examples, the Distinction Between Magnitude of Average Velocity Over an Interval of Time, and the Average Speed Over the Same Interval Concept: Average Velocity and Average Speed.
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