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title: "An electric cart of mass \\(m\\) uses a regenerative braking system that exerts a constant retarding force to bring the cart to rest from an initial speed \\(v_0\\) over a stopping distance \\(d\\). During this process, the total energy recovered by the system is \\(E_0\\) and the maximum instantaneous power absorbed by the system is \\(P_0\\). In a second test, the cart is brought to rest over the same stopping distance \\(d\\) from an initial speed of \\(2v_0\\) using a different constant retarding force. What are the total energy recovered \\(E’\\) and the maximum instantaneous power absorbed \\(P’\\) during the second test in terms of \\(E_0\\) and \\(P_0\\)?"
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url: "https://nerd-notes.com/ubq/119080/"
date_modified: "2026-08-18T04:48:41+00:00"
---

# An electric cart of mass \(m\) uses a regenerative braking system that exerts a constant retarding force to bring the cart to rest from an initial speed \(v_0\) over a stopping distance \(d\). During this process, the total energy recovered by the system is \(E_0\) and the maximum instantaneous power absorbed by the system is \(P_0\). In a second test, the cart is brought to rest over the same stopping distance \(d\) from an initial speed of \(2v_0\) using a different constant retarding force. What are the total energy recovered \(E’\) and the maximum instantaneous power absorbed \(P’\) during the second test in terms of \(E_0\) and \(P_0\)?

An electric cart of mass \(m\) uses a regenerative braking system that exerts a constant retarding force to bring the cart to rest from an initial speed \(v_0\) over a stopping distance \(d\). During this process, the total energy recovered by the system is \(E_0\) and the maximum instantaneous power absorbed by the system is \(P_0\). In a second test, the cart is brought to rest over the same stopping distance \(d\) from an initial speed of \(2v_0\) using a different constant retarding force. What are the total energy recovered \(E'\) and the maximum instantaneous power absorbed \(P'\) during the second test in terms of \(E_0\) and \(P_0\)?

- **A.** \(E' = 2E_0\) and \(P' = 4P_0\)
- **B.** \(E' = 4E_0\) and \(P' = 4P_0\)
- **C.** \(E' = 4E_0\) and \(P' = 8P_0\)
- **D.** \(E' = 8E_0\) and \(P' = 16P_0\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/119080/*