---
title: "A student performs two trials of a walking experiment on a flat, horizontal field. In Trial 1, the student walks a distance \\(L\\) due east and then a distance \\(L\\) due north. In Trial 2, the student walks a distance \\(1.5L\\) due east and then a distance \\(0.5L\\) due north. Let \\(D_1\\) and \\(D_2\\) represent the magnitudes of the net displacement for Trial 1 and Trial 2, respectively. Which of the following correctly compares the magnitudes of the displacements and provides a valid justification?"
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url: "https://nerd-notes.com/ubq/113931/"
date_modified: "2026-06-22T07:38:29+00:00"
---

# A student performs two trials of a walking experiment on a flat, horizontal field. In Trial 1, the student walks a distance \(L\) due east and then a distance \(L\) due north. In Trial 2, the student walks a distance \(1.5L\) due east and then a distance \(0.5L\) due north. Let \(D_1\) and \(D_2\) represent the magnitudes of the net displacement for Trial 1 and Trial 2, respectively. Which of the following correctly compares the magnitudes of the displacements and provides a valid justification?

A student performs two trials of a walking experiment on a flat, horizontal field. In Trial 1, the student walks a distance \(L\) due east and then a distance \(L\) due north. In Trial 2, the student walks a distance \(1.5L\) due east and then a distance \(0.5L\) due north. Let \(D_1\) and \(D_2\) represent the magnitudes of the net displacement for Trial 1 and Trial 2, respectively. Which of the following correctly compares the magnitudes of the displacements and provides a valid justification?

![Two separate x-y coordinate grids shown side-by-side. The left grid, labeled Trial 1, shows a solid arrow of length L along the positive x-axis and a second solid arrow of length L starting from the tip of the first and pointing in the positive y-direction. A dashed vector labeled D1 connects the origin to the final position. The right grid, labeled Trial 2, shows a solid arrow of length 1.5L along the positive x-axis and a second solid arrow of length 0.5L starting from the tip of the first and pointing in the positive y-direction. A dashed vector labeled D2 connects the origin to the final position.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1782113909-hbpePQ.jpg)

- **A.** \(D_2 > D_1\) because the magnitude of displacement is determined by the square root of the sum of the squares of the components, and \((1.5L)^2 + (0.5L)^2 > L^2 + L^2\).
- **B.** \(D_2 > D_1\) because the student covers a larger distance in a single cardinal direction in Trial 2 than in Trial 1.
- **C.** \(D_1 > D_2\) because a displacement vector is maximized when its perpendicular components are equal in magnitude for a fixed total distance traveled.
- **D.** \(D_1 = D_2\) because the total distance traveled by the student, which is the sum of the magnitudes of the individual segments, is \(2L\) in both trials.

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/113931/*