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title: "A particle of mass \\(m\\) is initially at rest at the origin \\((x,y) = (0,0)\\) at time \\(t = 0\\). The particle is acted upon by a time-dependent net force \\(\\vec{F}(t) = Ct\\,\\hat{i} + Dt^2\\,\\hat{j}\\), where \\(C\\) and \\(D\\) are positive constants. Which of the following expressions represents the particle’s trajectory \\(y(x)\\) for \\(x \\ge 0\\)?"
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url: "https://nerd-notes.com/ubq/117631/"
date_modified: "2026-08-04T07:49:24+00:00"
---

# A particle of mass \(m\) is initially at rest at the origin \((x,y) = (0,0)\) at time \(t = 0\). The particle is acted upon by a time-dependent net force \(\vec{F}(t) = Ct\,\hat{i} + Dt^2\,\hat{j}\), where \(C\) and \(D\) are positive constants. Which of the following expressions represents the particle’s trajectory \(y(x)\) for \(x \ge 0\)?

A particle of mass \(m\) is initially at rest at the origin \((x,y) = (0,0)\) at time \(t = 0\). The particle is acted upon by a time-dependent net force \(\vec{F}(t) = Ct\,\hat{i} + Dt^2\,\hat{j}\), where \(C\) and \(D\) are positive constants. Which of the following expressions represents the particle's trajectory \(y(x)\) for \(x \ge 0\)?

- **A.** \(\dfrac{D}{3m} \left(\dfrac{2mx}{C}\right)^{4/3}\)
- **B.** \(\dfrac{D}{12m} \left(\dfrac{6mx}{C}\right)^{4/3}\)
- **C.** \(\dfrac{D}{2m} \left(\dfrac{2mx}{C}\right)^{4/3}\)
- **D.** \(\dfrac{D}{m} \left(\dfrac{mx}{C}\right)^{4/3}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/117631/*