Question

The numerical value of the ratio of average velocity to average speed is
(A) Always less than one.
(B) Always equal to one.
(C) Always more than one.
(D) Equal to or less than one.

Answer 1

Hint:First we obtain the formula for average velocity and average speed. Then we compare both of them. Remember that displacement can-not be greater than distance. It can be either equal or less than the distance.

Complete step by step answer:
An object's average velocity is the total displacement separated by the total time taken. In other terms, it is the pace at which an entity from one location to another shifts its position. It is a vector quantity.The formula for average velocity is given by,
Average velocity = Total displacement / Total time
By dividing the total distances that the object travels by the total time that the object takes to travel these distances, is the average speed of an object.
The formula for average speed is,
Average speed = Total distance / Total time
Now, the ratio between average velocity and average speed is.
Average velocity / Average speed = Total displacement / Total distance. (Since the total time is common factor in both the form hence, it is get cancelled)
Now, we know that, Displacement can be equal or less than the distance but it can-not be greater than the distance. Hence, the ratio of “Total displacement / total distance” is always equal or less than one.
Hence, option D is correct.

Note:The ratio between average velocity and average speed is. Average velocity / Average speed = Total displacement / Total distance. Remember that the numerator part is smaller or equal to the denominator part. Hence, the ratio is always equal or less than one.