---
title: "At time \\(t = 0\\), a car traveling along a straight road at a constant speed \\(v_0\\) passes a stationary police cruiser. At that same instant, the cruiser begins pursuing the car from rest with an acceleration given by \\(a(t) = \\beta t\\), where \\(\\beta\\) is a positive constant. At the moment the cruiser catches up to the car, what is the speed of the cruiser?"
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url: "https://nerd-notes.com/ubq/120471/"
date_modified: "2026-08-23T04:39:01+00:00"
---

# At time \(t = 0\), a car traveling along a straight road at a constant speed \(v_0\) passes a stationary police cruiser. At that same instant, the cruiser begins pursuing the car from rest with an acceleration given by \(a(t) = \beta t\), where \(\beta\) is a positive constant. At the moment the cruiser catches up to the car, what is the speed of the cruiser?

At time \(t = 0\), a car traveling along a straight road at a constant speed \(v_0\) passes a stationary police cruiser. At that same instant, the cruiser begins pursuing the car from rest with an acceleration given by \(a(t) = \beta t\), where \(\beta\) is a positive constant. At the moment the cruiser catches up to the car, what is the speed of the cruiser?

- **A.** \(2v_0\)
- **B.** \(3v_0\)
- **C.** \(4v_0\)
- **D.** \(6v_0\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/120471/*