---
title: "A vehicle of mass \\(m\\) is initially at rest at position \\(x = 0\\) on a horizontal, frictionless track. Starting at time \\(t = 0\\), the engine delivers a constant net power \\(P_0\\) to accelerate the vehicle along the positive \\(x\\)-axis. Which of the following expressions represents the position \\(x(t)\\) of the vehicle as a function of time \\(t\\)?"
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url: "https://nerd-notes.com/ubq/120627/"
date_modified: "2026-08-23T04:42:17+00:00"
---

# A vehicle of mass \(m\) is initially at rest at position \(x = 0\) on a horizontal, frictionless track. Starting at time \(t = 0\), the engine delivers a constant net power \(P_0\) to accelerate the vehicle along the positive \(x\)-axis. Which of the following expressions represents the position \(x(t)\) of the vehicle as a function of time \(t\)?

A vehicle of mass \(m\) is initially at rest at position \(x = 0\) on a horizontal, frictionless track. Starting at time \(t = 0\), the engine delivers a constant net power \(P_0\) to accelerate the vehicle along the positive \(x\)-axis. Which of the following expressions represents the position \(x(t)\) of the vehicle as a function of time \(t\)?

- **A.** \(\sqrt{\dfrac{P_0 t^3}{2m}}\)
- **B.** \(\sqrt{\dfrac{4P_0 t^3}{9m}}\)
- **C.** \(\sqrt{\dfrac{2P_0 t^3}{m}}\)
- **D.** \(\sqrt{\dfrac{8P_0 t^3}{9m}}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/120627/*