Average Velocity From Displacement
A particle moves 8 m east and then 6 m north in a total time of 5 seconds along a flat surface, what is the magnitude of its average velocity?
Select the correct option:
Solution
2m/s
As explained in NCERT Class 11, Chapter 4 (Motion in a Plane), average velocity is the net displacement divided by the total time taken, where net displacement is the straight-line vector from start to finish. The eastward and northward legs are perpendicular, so the resultant displacement magnitude is √(8² + 6²) = √(64 + 36) = √100 = 10 m. Dividing by the total time, average velocity = 10/5 = 2 m/s. The option 2.8 m/s wrongly adds the path lengths (8 + 6 = 14) and divides by 5. The option 1.6 m/s uses only the 8 m leg divided by 5. The option 10 m/s mistakes displacement for velocity by omitting the time division. Plausibility check: average velocity uses displacement, not total path, so it must be at most the average speed of (14/5) = 2.8 m/s; the obtained 2 m/s is correctly smaller, confirming consistency with the displacement-based definition.
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About This Question
- Subject
- physics
- Chapter
- kinematics
- Topic
- average velocity from displacement
- Difficulty
- Medium
- Year
- 2025
Solution
Correct Answer:
2m/s
As explained in NCERT Class 11, Chapter 4 (Motion in a Plane), average velocity is the net displacement divided by the total time taken, where net displacement is the straight-line vector from start to finish. The eastward and northward legs are perpendicular, so the resultant displacement magnitude is √(8² + 6²) = √(64 + 36) = √100 = 10 m. Dividing by the total time, average velocity = 10/5 = 2 m/s. The option 2.8 m/s wrongly adds the path lengths (8 + 6 = 14) and divides by 5. The option 1.6 m/s uses only the 8 m leg divided by 5. The option 10 m/s mistakes displacement for velocity by omitting the time division. Plausibility check: average velocity uses displacement, not total path, so it must be at most the average speed of (14/5) = 2.8 m/s; the obtained 2 m/s is correctly smaller, confirming consistency with the displacement-based definition.
This medium difficulty physics question is from the chapter kinematics, covering the topic of average velocity from displacement. It appeared in the 2025 exam.
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