# 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?

# Answer:

Instantaneous velocity
is given by the first derivative of distance with respect to time i.e.,

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.

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