In one-dimensional motion, instantaneous speed is always equal to the magnitude of instantaneous vel

Question

In one-dimensional motion, instantaneous speed is always equal to the magnitude of instantaneous velocity. Is the same true for average speed and average velocity over an interval of time?

Professor PC Thomas Classes · Answer

Instantaneous speed is defined as the magnitude of instantaneous velocity ($|d\vec{r}/dt|$). Average speed is total path length divided by time interval, while the magnitude of average velocity is the magnitude of displacement divided by time. Since path length $\ge$ magnitude of displacement, average speed $\ge$ magnitude of average velocity.