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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 cab man 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?

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Given, the actual path length travelled is 23 km, displacement is 10 km and the time taken is 28 min. (a) Average speed of the taxi is given as, v avg = Total Path length Time Here, s is the total path length Substitute the values in above equation. v avg = Total Path length Time...
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Given, the actual path length travelled is 23 km, displacement is 10 km and the time taken is 28 min.

(a)

Average speed of the taxi is given as,

v avg = Total Path length Time

Here, s is the total path length

Substitute the values in above equation.

v avg = Total Path length Time = 23 km ( 28 min )( 1 h 60 min ) =49.3  km/h

Hence, the average speed of the taxi is 49.3  km/h .

(b)

Magnitude of the average velocity is given as,

v avg = Displacement Time

Substitute the values in the above equation.

v avg = Displacement Time = 10 km ( 28 min )( 1 h 60 min ) =21.4  km/h

(c)

From the calculation in (a) and (b), it is obtained that the average speed is not equal to the magnitude of average velocity.

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Tutor with 13 years of experience of teaching mathematics and Science

a) To find the avearage speed of the taxi, Given data,Total distance travelled: 23 km Total time taken: 28 min, 28/60=0.4666hr average speed = Total distance travelled / Total time taken =23/0.4666 =49.29km/h =50km/hr b) Distance between the hotel and the station = 10 km = Displacement of the car To...
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a) To find the avearage speed of the taxi, 

Given data,
Total distance travelled: 23 km

Total time taken: 28 min, 28/60=0.4666hr

average speed = Total distance travelled / Total time taken

=23/0.4666

=49.29km/h

=50km/hr

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

To find the magnitude of average velocity,

Average velocity =Displacement/ Total time taken
=10/0.4666

= 21.43km/h

hence, the average speed and average velocity are not equal.

 

 

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