Question

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 ?

Answer 1

a) Total distance travelled = 23 km
Total time taken = 28 min = $\frac{28}{60}$ h
Average speed of the taxi = $\frac{\text{Total distance travelled} }{\text{Total time taken}}$

= $\frac{23}{ (\frac{29}{60})}$ = 49.29 Km/h

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b) Distance between the hotel and the station = 10 km = Displacement of the car

∴ Average velocity = $\frac{10}{\frac{28}{60}}$= 21.43 km/h

Therefore, the two physical quantities (average speed and average velocity) are not equal.