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Q2.11: NCERT Physics - Part 1 MOTION IN A STRAIGHT LINE 2.11 Solution: In Exercises 2.9 and 2.10, we have carefully distinguished…
⚠️ Common Exam Traps & Conceptual Pitfalls
Students frequently assume that the path length $ds$ equals $|dx|$ for any time interval, and thus treat average speed as the magnitude of average velocity. Remember that $ds=|dx|$ holds only in the infinitesimal limit $dt\to0$; only then does instantaneous speed $v=ds/dt$ equal $|dx/dt|$, the magnitude of instantaneous velocity.
In Exercises 2.9 and 2.10, we have carefully distinguished between average speed and magnitude of average velocity. No such distinction is necessary when we consider instantaneous speed and magnitude of velocity. The instantaneous speed is always equal to the magnitude of instantaneous velocity. Why?
Step-by-Step Verified Solution
**Answer:** Because instantaneous speed and magnitude of instantaneous velocity are both defined over infinitesimally small time intervals where path length equals displacement magnitude.
**Step-by-Step Explanation:**
Over an infinitesimal time dt, the path length ds and displacement magnitude |dx| are equal (ds = |dx|). Therefore, instantaneous speed v = ds/dt equals |dx/dt| = magnitude of instantaneous velocity.
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