Question

Mark the correct statements:
A. The magnitude of the velocity of a particle is equal to its speed.
B. The magnitude of average velocity in an interval is equal to its average speed in that interval.
C. It is possible to have a situation in which the speed of a particle is always zero but the average speed is not zero.
D. It is possible to have a situation in which the speed of the particle is never zero but the average speed in an interval is zero.

Answer 1

Hint: To find the correct statements, check each of the options one by one. The options involve speed and velocity so recall the concepts of speed and velocity. Check for the factors on which speed and velocity depends and what are the similarities between them.

Complete step by step answer:
We check all the options one by one:

Option (A): Speed is distance travelled in a given time and velocity is distance travelled along a direction in a given time. So, velocity without direction is equal to speed. Therefore, the magnitude of velocity of a particle is equal to its speed. Thus, option (A) is correct.

Option (B): Average velocity in an interval can be defined as the total displacement of a body in a given time interval, while average speed is defined as total distance travelled by a body in a given time interval. Total distance might not be equal to total displacement of a body, for example if a body after travelling for a while, comes back to its initial position then its total displacement is zero but total distance will not be zero. So, we cannot say that the magnitude of average velocity in an interval is equal to its average speed in that interval. Therefore, option (B) is incorrect.

Option (C) : It is possible that for some instant or time the speed may be zero or we can say the particle is rest but for other instant the particle is moving, but if the speed of the particle is always zero then its average speed will also be zero as no distance will be travelled by the particle. Therefore, it is not possible to have a situation where the speed of the particle is zero and average speed is not zero, so option (C) is incorrect.

Option (D): If the speed of the particle is never zero, then there will be some distance travelled by the particle and total distance will not be zero. As, average speed is total distance travelled divided by the time interval, so, there will be some average speed. Therefore, it is not possible to have a situation in which the speed of the particle is never zero but the average speed in an interval is zero. Option (D) is incorrect.

So, the correct answer is “Option A”.

Note:
Speed is a scalar quantity while velocity is a vector quantity that is speed has only magnitude and velocity has both magnitude and direction. Speed is how fast a body is moving and velocity is how fast an object is moving and in which direction that velocity is related to displacement of the body and speed is related to total distance travelled by the body.