---
title: "A cart moves along a straight horizontal track with a velocity described by the function \\(v(t) = v_0\\left(1 – \\dfrac{t}{\\tau}\\right)^3\\), where \\(v_0 = 16\\text{ m/s}\\) and \\(\\tau = 3.0\\text{ s}\\). The cart moves according to this relationship from \\(t = 0\\) to \\(t = 2\\tau = 6.0\\text{ s}\\). What is the total distance traveled by the cart from \\(t = 0\\) to \\(t = 6.0\\text{ s}\\)?"
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url: "https://nerd-notes.com/ubq/123960/"
date_modified: "2026-09-28T13:28:01+00:00"
---

# A cart moves along a straight horizontal track with a velocity described by the function \(v(t) = v_0\left(1 – \dfrac{t}{\tau}\right)^3\), where \(v_0 = 16\text{ m/s}\) and \(\tau = 3.0\text{ s}\). The cart moves according to this relationship from \(t = 0\) to \(t = 2\tau = 6.0\text{ s}\). What is the total distance traveled by the cart from \(t = 0\) to \(t = 6.0\text{ s}\)?

A cart moves along a straight horizontal track with a velocity described by the function \(v(t) = v_0\left(1 - \dfrac{t}{\tau}\right)^3\), where \(v_0 = 16\text{ m/s}\) and \(\tau = 3.0\text{ s}\). The cart moves according to this relationship from \(t = 0\) to \(t = 2\tau = 6.0\text{ s}\). What is the total distance traveled by the cart from \(t = 0\) to \(t = 6.0\text{ s}\)?

- **A.** \(0\text{ m}\)
- **B.** \(12\text{ m}\)
- **C.** \(24\text{ m}\)
- **D.** \(48\text{ m}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/123960/*