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title: "A particle moves along the \\(x\\)-axis with velocity given by \\(v(t) = c(t – t_1)(t – t_2)\\), where \\(c\\), \\(t_1\\), and \\(t_2\\) are positive constants such that \\(0 < t_1 < t_2\\). Let \\(t_m = \\dfrac{t_1 + t_2}{2}\\). Which row in the table correctly describes the behavior of the particle's speed during the interval \\(t_1 < t < t_m\\), its speed during the interval \\(t_m < t < t_2\\), and the change in its position \\(x(t)\\) during the interval \\(t_m < t < t_2\\)?"
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url: "https://nerd-notes.com/ubq/123966/"
date_modified: "2026-09-28T13:28:20+00:00"
---

# A particle moves along the \(x\)-axis with velocity given by \(v(t) = c(t – t_1)(t – t_2)\), where \(c\), \(t_1\), and \(t_2\) are positive constants such that \(0 < t_1 < t_2\). Let \(t_m = \dfrac{t_1 + t_2}{2}\). Which row in the table correctly describes the behavior of the particle's speed during the interval \(t_1 < t < t_m\), its speed during the interval \(t_m < t < t_2\), and the change in its position \(x(t)\) during the interval \(t_m < t < t_2\)?

A particle moves along the \(x\)-axis with velocity given by \(v(t) = c(t - t_1)(t - t_2)\), where \(c\), \(t_1\), and \(t_2\) are positive constants such that \(0 < t_1 < t_2\). Let \(t_m = \dfrac{t_1 + t_2}{2}\). Which row in the table correctly describes the behavior of the particle's speed during the interval \(t_1 < t < t_m\), its speed during the interval \(t_m < t < t_2\), and the change in its position \(x(t)\) during the interval \(t_m < t < t_2\)?

- **A.** Speed (\(t_1 < t < t_m\)): Increasing | Speed (\(t_m < t < t_2\)): Decreasing | Position \(x(t)\) (\(t_m < t < t_2\)): Decreasing
- **B.** Speed (\(t_1 < t < t_m\)): Decreasing | Speed (\(t_m < t < t_2\)): Increasing | Position \(x(t)\) (\(t_m < t < t_2\)): Increasing
- **C.** Speed (\(t_1 < t < t_m\)): Increasing | Speed (\(t_m < t < t_2\)): Decreasing | Position \(x(t)\) (\(t_m < t < t_2\)): Increasing
- **D.** Speed (\(t_1 < t < t_m\)): Decreasing | Speed (\(t_m < t < t_2\)): Decreasing | Position \(x(t)\) (\(t_m < t < t_2\)): Decreasing

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/123966/*