Physics
Physics
Problem
Show that, for motion along a straight line without any change in direction, the numerical value of average speed equals the magnitude of average velocity.Intuitive explanation
The key insight is recognizing what "no change in direction" really means: the object travels along a single straight path without ever reversing or turning back. When motion is strictly one-directional, the total distance traveled equals the magnitude of the displacement—they're the same path length. Since average speed uses total distance and average velocity uses displacement magnitude, dividing each by the same time interval gives you identical numerical values. The proof hinges on this geometric equivalence.
Intuitive explanation
The key insight is recognizing what "no change in direction" really means: the object travels along a single straight path without ever reversing or turning back. When motion is strictly one-directional, the total distance traveled equals the magnitude of the displacement—they're the same path length. Since average speed uses total distance and average velocity uses displacement magnitude, dividing each by the same time interval gives you identical numerical values. The proof hinges on this geometric equivalence.