Physics
Physics
Problem
A scooterist rides along a straight road covering the same distance twice—first from town A to town B and then back to town A—but at two different constant speeds. Answer the following questions about the journey without performing any numerical calculation. a. (i) Define average speed and average velocity for the complete round trip in words only. b. (ii) Explain qualitatively why the numerical value of the average speed for the round trip cannot be the simple arithmetic mean of the two individual speeds used on the onward and return journeys. c. (iii) Discuss, with reasons, whether the average velocity for the entire journey is zero, positive, or negative. d. (iv) Using logical argument (no algebra needed), justify why an average taken over equal distances but unequal speeds is closer to the lower of the two speeds.Intuitive explanation
This problem is about average velocity and average speed, and the key insight is that these two quantities are not the same when you travel the same distance at different speeds. Even though you cover equal distances at each speed, the time spent at each speed is different—you linger longer at the slower speed. This means your overall average speed is closer to the slower speed than a simple arithmetic mean would suggest, and your net displacement determines your average velocity for the round trip.
Intuitive explanation
This problem is about average velocity and average speed, and the key insight is that these two quantities are not the same when you travel the same distance at different speeds. Even though you cover equal distances at each speed, the time spent at each speed is different—you linger longer at the slower speed. This means your overall average speed is closer to the slower speed than a simple arithmetic mean would suggest, and your net displacement determines your average velocity for the round trip.