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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(N/A) Instantaneous velocity is defined as the limit of average velocity as the time interval $\Delta t$ approaches zero,given by $v = \frac{dx}{dt}$.
In this infinitesimal time interval $dt$,the path length covered by the particle is equal to the magnitude of its displacement because the particle does not have enough time to change its direction of motion.
Since instantaneous speed is the magnitude of the rate of change of distance and instantaneous velocity is the rate of change of displacement,and because $dx = |dx|$ for an infinitesimal interval,the instantaneous speed is always equal to the magnitude of the instantaneous velocity.

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