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Q2.9: NCERT Physics - Part 1 MOTION IN A STRAIGHT LINE 2.9 Solution: Explain clearly, with examples, the distinction between: (a)…
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In one‑dimensional motion, the displacement magnitude is the absolute difference between the final and initial positions, whereas the path length is the sum of all absolute displacements over each segment. If the particle reverses direction, the path length exceeds the displacement magnitude, so the average speed exceeds the magnitude of the average velocity. Always check for direction changes before assuming equality.
Explain clearly, with examples, the distinction between: (a) magnitude of displacement (sometimes called distance) over an interval of time, and the total length of path covered by a particle over the same interval; (b) 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].
Step-by-Step Verified Solution
**Answer:** (a) Displacement magnitude � path length. (b) Average speed � magnitude of average velocity. Equality when motion is in a straight line without reversal.
**Step-by-Step Explanation:**
(a) Displacement is the shortest distance between initial and final positions. Path length is the actual distance travelled. Example: If a particle moves 5 m forward and 3 m backward, displacement = 2 m, path length = 8 m.
(b) Average velocity = displacement/time, average speed = path length/time. Since displacement � path length, average speed � magnitude of average velocity. Equality holds for motion in a straight line without reversal. [citation:19]
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