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Instead of the definition given in Eq. 2-13, we might have defined average speed as the magnitude of the average velocity. Are the definitions different? Give examples to support your answer.

Instead of the definition given in Eq. 2-13, we might have defined average speed as the magnitude of the average velocity. Are the definitions different? Give examples to support your answer.

Grade:upto college level

1 Answers

Deepak Patra
askIITians Faculty 471 Points
6 years ago
The magnitude of average velocity is not the average speed because for a particular interval, the average velocity depends on the displacement of the particle; while on the other hand, the average speed depends on the distance travelled by the particle.
From definition, we have
average\ speed = \frac{total\ distance\ travelled}{elapsed\ time}
average\ velocity = \frac{net\ displacement}{elapsed\ time}
Therefore, for a particular time interval, it is not necessary that the distance traveled by the particle is equal to its displacement. Thus, the average speed cannot be taken to be as the magnitude of average velocity.
Say for instance, a car changes its position from some initial point x1 to a point x2 in
10 sec such that the magnitude of displacement is say 1 km. However the distance travelled by the car during the same interval is 2 km. Therefore the magnitude of the average velocity of the car is the magnitude of displacement divided by the time i.e 0.1km/s. .
The average speed of the car is the distance traveled by the car in elapsed time i.e. .0.2 km/s. Thus, one can easily see that the magnitude of the average velocity does not match to that with the average speed.

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