Question

Under which of the following conditions is the magnitude of the average velocity of a particle moving in one dimension smaller than the average speed over some time interval?a. A particle moves in the +x direction and then reverses the direction of its motion.b. A particle moves in the +x direction without reversing.c. There are no conditions for which this is true.d. A particle moves in the -x direction without reversing.

Answer 1

Answer: A.

Explanation:

For example,

If you start from 0 and move 5 units in the positive x axis and reverse to return to 2 units from 0, your displacement will be 2 units but distance covered will be 8 units.

Average velocity = Displacement / time

= 2 / time

Average speed = distance / time

= 8 / time

Here, time will be the same, so you can see that magnitude of the average velocity of a particle moving in one dimension smaller than the average speed over some time interval.

Answer 2

The given condition in the question is possible only on condition if a particle moves in the +x direction and then reverses the direction of its motion.

The average speed of particle would:

• average speed =  $\dfrac{\text{distance traveled}}{\text{time taken}}$

and the average speed of particle would be:

• average velocity =  $\dfrac{\text{total displacement}}{\text{time taken}}$  

Therefore, In the given condition that says that average velocity to be less than the average speed would be:

1. => displacement must be less than the total distance traveled
2. => car has to reverse back from its initial direction of motion

Thus, the correct answer would be if - a particle moves in the +x direction and then reverses the direction of its motion.

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