A passenger arriving in a new town wishes to go from the station to a hotel located to 10km away on 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 ?

Explanation

Here, actual path length travelled, S = 23 km, displacement = 10km, time taken, t = 28 min = 28/60 h
(a) Average speed of a taxi
`= ("actual path length")/("time taken") = (23)/(28//60)`
= 49.3 km/hr
(b) Magnitude of average elocity
`= ("displacement")/("time taken") = (10)/((28//60)) = 21.4` km/hr
The average speed is not equal to the magnitude of the average velocity. The two are equal for the motion of taxi along a straight path in one direction.