The instantaneous speed is always equal to the magnitude of instantaneous velocity. Why?

Explanation

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.