---
title: "An object moves along the \\(x\\)-axis such that its position as a function of time \\(t\\) is given by \\(x(t) = v_0 t e^{-\\beta t}\\), where \\(v_0\\) and \\(\\beta\\) are positive constants. Consider the speeds \\(s_1\\), \\(s_2\\), \\(s_3\\), and \\(s_4\\) of the object at times \\(t_1 = 0\\), \\(t_2 = \\dfrac{1}{\\beta}\\), \\(t_3 = \\dfrac{2}{\\beta}\\), and \\(t_4 = \\dfrac{3}{\\beta}\\), respectively. Which of the following correctly ranks the speeds of the object from greatest to least?"
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url: "https://nerd-notes.com/ubq/120473/"
date_modified: "2026-08-23T04:39:02+00:00"
---

# An object moves along the \(x\)-axis such that its position as a function of time \(t\) is given by \(x(t) = v_0 t e^{-\beta t}\), where \(v_0\) and \(\beta\) are positive constants. Consider the speeds \(s_1\), \(s_2\), \(s_3\), and \(s_4\) of the object at times \(t_1 = 0\), \(t_2 = \dfrac{1}{\beta}\), \(t_3 = \dfrac{2}{\beta}\), and \(t_4 = \dfrac{3}{\beta}\), respectively. Which of the following correctly ranks the speeds of the object from greatest to least?

An object moves along the \(x\)-axis such that its position as a function of time \(t\) is given by \(x(t) = v_0 t e^{-\beta t}\), where \(v_0\) and \(\beta\) are positive constants. Consider the speeds \(s_1\), \(s_2\), \(s_3\), and \(s_4\) of the object at times \(t_1 = 0\), \(t_2 = \dfrac{1}{\beta}\), \(t_3 = \dfrac{2}{\beta}\), and \(t_4 = \dfrac{3}{\beta}\), respectively. Which of the following correctly ranks the speeds of the object from greatest to least?

- **A.** \(s_1 > s_2 > s_3 > s_4\)
- **B.** \(s_1 > s_2 > s_4 > s_3\)
- **C.** \(s_1 > s_4 > s_3 > s_2\)
- **D.** \(s_1 > s_3 > s_4 > s_2\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/120473/*