Question

There is a distinction between average speed and the magnitude of average velocity. Give an example that illustrates the difference between these two quantities.

Answer 1

An example that illustrates the difference is the circular motion

Explanation:

Let's start by reminding the definition of the two quantities:

- Speed is a scalar quantity that tells "how fast" an object is moving, regardless of its direction of motion.

Speed can be  calculate as:

$speed = \frac{d}{t}$

where:

d is the distance travelled

t is the time taken

- Velocity is instead a vector quantity, given by:

$velocity = \frac{d}{t}$

where;

d is the displacement of the object (displacement is a a vector connecting the initial position to the final position of motion)

t is the time taken

Since it is a vector, velocity has both a magnitude and a direction, therefore it also takes into account the direction of motion of the object.

For an object in motion in a straight line, speed and velocity are the same. However, this is not always the case.

In fact, an example of motion in which the two quantities are different is the circular motion. Consider for example the object making one complete revolution along the circle. Therefore, its average speed is the ratio between the length of the perimeter (the distance) divided by the time taken:

$speed = \frac{2\pi r}{t}$

where r is the radius of the circle.

However, the displacement of the object is zero (because the object returns to the starting point), and so the average velocity is also zero:

$velocity = \frac{0}{t}=0$

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