A passenger arriving in a new town wishes to go from the station to a hotel located 10 km away on a straight road from the station. A dishonest cabman takes him along a circuitous path 23 km long and reaches the hotel in 28 min. What is (a) the average speed of the taxi, (b) the magnitude of average velocity? Are the two equal?
Average speed of the taxi = 49.3 km/h (approximately)
Magnitude of average velocity = 21.4 km/h (approximately)
Explanation
This question tests the fundamental difference between speed and velocity. Average speed depends on the total path length covered, while average velocity depends only on the displacement (shortest distance between initial and final positions). Since the cabman took a circuitous route, the path length (23 km) exceeds the displacement (10 km), making average speed greater than the magnitude of average velocity.