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Motion in a Straight Line — Physics STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 SciencePhysicsMotion in a Straight Line3 Marks
Question
In Exercises $3.13$ and $3.14$, 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?
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Answer

Instantaneous velocity is given by the first derivative of distance with respect to time i.e., $V_{in} = dx/dt$ Here, the time interval dt is so small that it is assumed that the particle does not change its direction of motion. As a result, both the total path length and magnitude of displacement become equal is this interval of time. Therefore, instantaneous speed is always equal to instantaneous velocity.

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