Which statement correctly contrasts average velocity and average speed?

Which statement correctly contrasts average velocity and average speed?

• A. They are always equal regardless of path
• B. Average speed is not the magnitude of the average velocity unless the object has moved in a straight line
• C. Average velocity equals distance over time
• D. Average speed equals displacement over time

Answer: (B)

Average speed and average velocity come from two different ways of measuring motion. Average speed uses total distance traveled divided by total time, while average velocity uses displacement—the straight-line distance from where you started to where you ended—divided by total time. If you move along a straight line in one direction without turning back, distance and displacement are the same, so the magnitudes of average speed and average velocity match. But for any curved or back-and-forth path, the distance traveled is greater than the straight-line displacement, so the average speed will be larger than the magnitude of the average velocity. That’s why this statement is correct: average speed is not the magnitude of the average velocity unless the motion is along a straight line. The other ideas don’t fit because velocity uses displacement over time (not distance), and speed uses distance over time (not displacement).

Average speed and average velocity come from two different ways of measuring motion. Average speed uses total distance traveled divided by total time, while average velocity uses displacement—the straight-line distance from where you started to where you ended—divided by total time.

If you move along a straight line in one direction without turning back, distance and displacement are the same, so the magnitudes of average speed and average velocity match. But for any curved or back-and-forth path, the distance traveled is greater than the straight-line displacement, so the average speed will be larger than the magnitude of the average velocity. That’s why this statement is correct: average speed is not the magnitude of the average velocity unless the motion is along a straight line.

The other ideas don’t fit because velocity uses displacement over time (not distance), and speed uses distance over time (not displacement).