---
title: "Four carts, labeled W, X, Y, and Z, travel along a straight, horizontal track. At time \\(t = 0\\), each cart is traveling with an initial speed \\(v_i\\) and begins to decelerate with a constant acceleration of magnitude \\(a\\) until it comes completely to rest. The initial speeds and deceleration magnitudes for each cart are given in the table.  | Cart | Initial Speed | Deceleration Magnitude | | :— | :— | :— | | W | \\(v_0\\) | \\(a_0\\) | | X | \\(2v_0\\) | \\(a_0\\) | | Y | \\(2v_0\\) | \\(4a_0\\) | | Z | \\(3v_0\\) | \\(6a_0\\) |  Which of the following correctly ranks the total stopping distance \\(\\Delta x\\) traveled by each cart from greatest to least?"
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url: "https://nerd-notes.com/ubq/120472/"
date_modified: "2026-08-23T04:39:02+00:00"
---

# Four carts, labeled W, X, Y, and Z, travel along a straight, horizontal track. At time \(t = 0\), each cart is traveling with an initial speed \(v_i\) and begins to decelerate with a constant acceleration of magnitude \(a\) until it comes completely to rest. The initial speeds and deceleration magnitudes for each cart are given in the table.

| Cart | Initial Speed | Deceleration Magnitude |
| :— | :— | :— |
| W | \(v_0\) | \(a_0\) |
| X | \(2v_0\) | \(a_0\) |
| Y | \(2v_0\) | \(4a_0\) |
| Z | \(3v_0\) | \(6a_0\) |

Which of the following correctly ranks the total stopping distance \(\Delta x\) traveled by each cart from greatest to least?

Four carts, labeled W, X, Y, and Z, travel along a straight, horizontal track. At time \(t = 0\), each cart is traveling with an initial speed \(v_i\) and begins to decelerate with a constant acceleration of magnitude \(a\) until it comes completely to rest. The initial speeds and deceleration magnitudes for each cart are given in the table.

| Cart | Initial Speed | Deceleration Magnitude |
| :--- | :--- | :--- |
| W | \(v_0\) | \(a_0\) |
| X | \(2v_0\) | \(a_0\) |
| Y | \(2v_0\) | \(4a_0\) |
| Z | \(3v_0\) | \(6a_0\) |

Which of the following correctly ranks the total stopping distance \(\Delta x\) traveled by each cart from greatest to least?

- **A.** \(\Delta x_X > \Delta x_W > \Delta x_Y = \Delta x_Z\)
- **B.** \(\Delta x_Z > \Delta x_Y > \Delta x_X > \Delta x_W\)
- **C.** \(\Delta x_Z > \Delta x_W = \Delta x_Y > \Delta x_X\)
- **D.** \(\Delta x_X > \Delta x_W = \Delta x_Y > \Delta x_Z\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/120472/*