Question

12. Sarah walks 2 kilometers north from her house to the grocery store. Then, she leaves the grocery store and walks 3 kilometers further north to her grandma’s house. She finally leaves her grandma’s house and walks home. b. What is Sarah’s distance? a. What is Sarah’s displacement?

Answer 1

a. distance: 10 km

The distance covered is equal to the sum of the distance of each part of the journey.

In this case, Sarah's trip consists of three parts:

- 2 km north from the house to the grocery store

- 3 km north to grandma's house

- 5 km back to reach home

So the distance covered is the sum of all these parts:

d = 2 km + 3 km + 5 km = 10 km

b. displacement: 0

Instead, displacement is defined as the distance (measured in a straight line) between the final point of the motion and the initial point of the motion. So displacement does not depend on the path taken by the object, but only on the final and initial position.

Here we have:

- Final position of Sarah's journey: home

- Initial position of Sarah's journey: home

So, the displacement is zero, because the final point corresponds to the initial point.