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title: "A block of mass \\(m_0\\) slides along a frictionless horizontal surface with initial kinetic energy \\(K_0\\). It undergoes a completely inelastic collision with a mass-accumulating target initially at rest. During the collision process, which lasts from time \\(t = 0\\) to \\(t = T\\), the total mass of the combined object increases according to the function \\(m(t) = m_0 e^{kt}\\), where \\(k\\) is a positive constant. Assuming no external horizontal forces act on the system, what is the final kinetic energy of the combined mass at time \\(t = T\\)?"
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url: "https://nerd-notes.com/ubq/117560/"
date_modified: "2026-08-04T07:49:05+00:00"
---

# A block of mass \(m_0\) slides along a frictionless horizontal surface with initial kinetic energy \(K_0\). It undergoes a completely inelastic collision with a mass-accumulating target initially at rest. During the collision process, which lasts from time \(t = 0\) to \(t = T\), the total mass of the combined object increases according to the function \(m(t) = m_0 e^{kt}\), where \(k\) is a positive constant. Assuming no external horizontal forces act on the system, what is the final kinetic energy of the combined mass at time \(t = T\)?

A block of mass \(m_0\) slides along a frictionless horizontal surface with initial kinetic energy \(K_0\). It undergoes a completely inelastic collision with a mass-accumulating target initially at rest. During the collision process, which lasts from time \(t = 0\) to \(t = T\), the total mass of the combined object increases according to the function \(m(t) = m_0 e^{kt}\), where \(k\) is a positive constant. Assuming no external horizontal forces act on the system, what is the final kinetic energy of the combined mass at time \(t = T\)?

- **A.** \(K_0 e^{kT}\)
- **B.** \(K_0 e^{-kT}\)
- **C.** \(K_0 e^{-2kT}\)
- **D.** \(K_0 (1 - e^{-kT})\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/117560/*