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title: "A test sled on a straight track enters a braking zone at time \\(t = 0\\) with an initial speed \\(v_0\\) and experiences a time-dependent deceleration given by \\(a(t) = -c t\\), where \\(c\\) is a positive constant. The sled comes to rest after traveling a total stopping distance \\(D_1\\). If the sled enters the braking zone with an initial speed of \\(3v_0\\) under the same deceleration function, what is the new total stopping distance in terms of \\(D_1\\)?"
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url: "https://nerd-notes.com/ubq/120481/"
date_modified: "2026-08-23T04:39:04+00:00"
---

# A test sled on a straight track enters a braking zone at time \(t = 0\) with an initial speed \(v_0\) and experiences a time-dependent deceleration given by \(a(t) = -c t\), where \(c\) is a positive constant. The sled comes to rest after traveling a total stopping distance \(D_1\). If the sled enters the braking zone with an initial speed of \(3v_0\) under the same deceleration function, what is the new total stopping distance in terms of \(D_1\)?

A test sled on a straight track enters a braking zone at time \(t = 0\) with an initial speed \(v_0\) and experiences a time-dependent deceleration given by \(a(t) = -c t\), where \(c\) is a positive constant. The sled comes to rest after traveling a total stopping distance \(D_1\). If the sled enters the braking zone with an initial speed of \(3v_0\) under the same deceleration function, what is the new total stopping distance in terms of \(D_1\)?

- **A.** \(3 D_1\)
- **B.** \(3\sqrt{3}\,D_1\)
- **C.** \(9 D_1\)
- **D.** \(27 D_1\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/120481/*