A man walks on a straight road from his home to a market 2.5 km away with a speed of 5 km h. Finding the market closed, he instantly turns and walks back home with a speed of 7.5 km h. What is the
magnitude of average velocity, and
average speed of the man over the interval of time (i) 0 to 30 min, (ii) 0 to 50 min, (iii) 0 to 40 min? [Note: You will appreciate from this exercise why it is better to define average speed as total path length divided by time, and not as magnitude of average velocity. You would not like to tell the tired man on his return home that his average speed was zero!]
Explanation
This problem illustrates the key difference between average velocity and average speed. Average velocity depends on displacement (final position minus initial position), while average speed depends on total path length traveled. When the man returns home, his displacement is zero but he has walked a considerable distance. The textbook note emphasizes why average speed is defined as total path length divided by time - telling a tired man his average speed was zero would be misleading!