Let's break down the problem step by step from your image:

a. Forward 5 steps:

The distance walked is 2.90 meters.

b. Turn 90° left and walk 2 steps:

The distance walked here is 1.50 meters.

c. Turn 90° left and walk 3 steps:

The distance walked here is 1.75 meters.

d. Turn 90° left and walk 4 steps:

The distance walked here is 2.10 meters.

e. Draw vector arrows:

The image shows a closed path in the shape of a rectangle, with arrows representing each part of the walk.

f. Measured Displacement:

Displacement is the straight-line distance from the origin to the final position. Since the shape in the diagram is a closed rectangle, and you end where you started, the measured displacement is 0 meters.

g. Total Distance:

The total distance is the sum of all the individual distances: $\text{Distance} = 2.90 \, m + 1.50 \, m + 1.75 \, m + 2.10 \, m = 8.25 \, \text{meters}$

h. Calculated Displacement:

Since the path forms a complete rectangle and ends back at the origin, the calculated displacement (straight-line distance from start to end) is also 0 meters. Displacement considers only the initial and final position, and in this case, they are the same.

i. Comparison:

Yes, the calculated displacement matches the measured displacement of 0 meters. This happens because displacement is a vector quantity that depends only on the initial and final positions, not the actual path taken. Since you returned to the origin, your displacement is zero, even though you walked a total distance of 8.25 meters.

Review: Difference Between Distance and Displacement

• Distance is a scalar quantity and measures the total length of the path traveled.
• Displacement is a vector quantity and measures the straight-line distance between the starting and ending points, along with the direction.

Let me know if you need further clarification on any part! Here are some follow-up questions to expand your understanding:

1. What would happen to the displacement if you hadn't returned to the origin?
2. How would you calculate displacement if the path wasn't rectangular?
3. What real-life situations could have large distances but zero displacements?
4. Can displacement be greater than the distance traveled?
5. Why is displacement considered a vector while distance is not?

Tip:

In problems involving vectors, always remember that direction matters for displacement but not for distance.