Which statement is true about average speed and average velocity?

• A. Average speed is based on distance traveled; average velocity is based on displacement.
• B. Average speed and average velocity are both based on distance.
• C. Both are based on displacement.
• D. Average speed is based on displacement; average velocity is based on distance.

Answer: (A)

The main idea here is that average speed and average velocity use different measures of how far you’ve moved. Average speed is total distance traveled divided by total time, so it’s a scalar and only cares about how much ground you covered, not the direction. Average velocity is displacement divided by total time, which means it uses the straight-line distance from where you started to where you ended and includes direction, making it a vector.

For example, if you walk 100 m east in 50 s, then stop for a while, your total distance is 100 m and total time is 50 s, so the average speed is 100/50 = 2 m/s. Your displacement is 100 m east, and over the same 50 s, the average velocity is 100/50 = 2 m/s east. If you instead go out and come back to your starting point, the distance might be 200 m, but the displacement is zero, so the average speed would be 200/t while the average velocity would be 0. This shows why the statement that average speed is based on distance and average velocity is based on displacement is the correct one.