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title: "Frame \\(A\\) moves with constant velocity \\(v_0\\) relative to the ground along a straight line. At time \\(t = 0\\), the origins of frame \\(A\\) and frame \\(B\\) coincide at \\(x = 0\\), and frame \\(B\\) is at rest relative to frame \\(A\\). Frame \\(B\\) accelerates relative to frame \\(A\\) with acceleration \\(a_{B/A}(t) = bt\\), where \\(b\\) is a positive constant. Which of the following expressions represents the position of the origin of frame \\(B\\) relative to the ground, \\(x_{B/G}(t)\\), as a function of time \\(t\\)?"
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url: "https://nerd-notes.com/ubq/117546/"
date_modified: "2026-08-04T07:48:59+00:00"
---

# Frame \(A\) moves with constant velocity \(v_0\) relative to the ground along a straight line. At time \(t = 0\), the origins of frame \(A\) and frame \(B\) coincide at \(x = 0\), and frame \(B\) is at rest relative to frame \(A\). Frame \(B\) accelerates relative to frame \(A\) with acceleration \(a_{B/A}(t) = bt\), where \(b\) is a positive constant. Which of the following expressions represents the position of the origin of frame \(B\) relative to the ground, \(x_{B/G}(t)\), as a function of time \(t\)?

Frame \(A\) moves with constant velocity \(v_0\) relative to the ground along a straight line. At time \(t = 0\), the origins of frame \(A\) and frame \(B\) coincide at \(x = 0\), and frame \(B\) is at rest relative to frame \(A\). Frame \(B\) accelerates relative to frame \(A\) with acceleration \(a_{B/A}(t) = bt\), where \(b\) is a positive constant. Which of the following expressions represents the position of the origin of frame \(B\) relative to the ground, \(x_{B/G}(t)\), as a function of time \(t\)?

- **A.** \(x_{B/G}(t) = v_0 t + \dfrac{1}{2}b t^2\)
- **B.** \(x_{B/G}(t) = v_0 t + \dfrac{1}{3}b t^3\)
- **C.** \(x_{B/G}(t) = v_0 t + \dfrac{1}{2}b t^3\)
- **D.** \(x_{B/G}(t) = v_0 t + \dfrac{1}{6}b t^3\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/117546/*