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Instantaneous Velocity and Instantaneous Speed Instantaneous velocity describes how fast an object is moving at different instants of time in a given time interval. It is also defined as average velocity for an infinitely small time interval.
Here lim is taking operation of taking limit with time tending towards 0 or infinitely small. dx / dt is differential coefficient – Rate of change of position with respect to time at an instant.
Instantaneous speed is the magnitude of velocity. Instantaneous speed at an instant is equal to the magnitude of the instantaneous velocity at that instant.