Question

Distinguish between the average speed and the average velocity.
a) Average speed is total displacement per unit time while average velocity is total distance travelled per unit time.
b) Average speed is total distance travelled per unit time while average velocity is total displacement per unit time.
c) Average speed is vector while average velocity is scalar quantity.
d) All of the above.

Answer 1

Hint: To solve this question, we need to have a clear understanding of scalar and vector quantities. Then we will check that among velocity, speed, distance and displacement, which one are scalar and which one are vector which will lead us to the final conclusion.

Complete step by step solution:
We will first see the difference between a scalar and vector quantity. A scalar quantity is one which only denotes the magnitude and vector denotes both magnitude and direction of the object.
Now, let us suppose there is a circular track of diameter D and a girl is standing at point A. She travels along the path ABC to reach a point C in time t after covering a distance equal to the semi perimeter of the circular track.

So, here the total distance covered by the girl will be $\dfrac{\pi D}{2}$, whereas net displacement will be the shortest path between the initial and final points and that will be equal to the diameter of the track. And the time taken in both the cases, t is same.
The formula for average speed is given by $v_{avg}=\dfrac{d}{t}$, where d is the total distance covered and t is the time taken. Whereas the formula for average velocity is given by $\vec{v}_{avg}=\dfrac{\vec{d}}{t}$, where $\vec{d}$ is the net displacement.
Therefore, in the above example $v_{avg}=\dfrac{\pi D}{2t}$ and $\vec{v}_{avg}=\dfrac{D}{t}$.
We can also summarize the differences between the average velocity and average speed in the following tabular column

Average velocity $\vec{v}_{avg}$	Average speed $v_{avg}$
It is a vector quantity i.e. have both magnitude and direction	It is a scalar quantity i.e. have only magnitude
It is given by the net displacement covered per unit time	It is given by the total distance covered per unit time
It can be zero or negative based on the final position and direction of movement of the object	It can be zero if the object doesn’t cover any distance but can never be negative
It is a path independent	It is path dependent

Hence, option b is the correct answer.

Note: The concept of scalar and vector quantities should be clear. And we should note that division or multiplication of a scalar quantity with a vector quantity, yields a vector quantity. That is why average velocity is calculated by dividing net displacement from time where also net displacement is a vector quantity and the same goes for the speed.