Neco 2022 Further Mathematics Question 47

Practice objective / multiple choice question 47 from the 2022 Neco Further Mathematics examination.

Neco 2022 Further Mathematics Objective / Multiple Choice Hard Difficulty
Question 47 NECO • 2022 • FURTHER_MATHEMATICS • objective

An object of mass \(2\ \text{kg}\) moves along a straight line with acceleration \(a(t)=6t-4\ \text{m s}^{-2}\) for \(t\ge0\). At \(t=0\) the object is at the origin and at rest. (i) Find its speed when it reaches the position \(x=10\ \text{m}\). (ii) From \(x=10\ \text{m}\) to \(x=20\ \text{m}\) the surface is rough, giving a kinetic friction coefficient \(\mu=0.2\). After \(x=20\ \text{m}\) the object moves on a smooth surface but is acted on by a constant retarding force of \(5\ \text{N}\) opposite its motion. Determine the additional distance beyond \(x=20\ \text{m}\) that the object travels before coming to rest.

Answer Options

A. Speed at \\(x=10\\) \\(\\approx17.2\\ \\text{m s}^{-1}\\); additional stopping distance \\(\\approx45.6\\ \\text{m}\\)
B. Speed at \\(x=10\\) \\(\\approx12.0\\ \\text{m s}^{-1}\\); additional stopping distance \\(\\approx35.2\\ \\text{m}\\)
C. Speed at \\(x=10\\) \\(\\approx13.5\\ \\text{m s}^{-1}\\); additional stopping distance \\(\\approx38.0\\ \\text{m}\\)
Correct Answer D. Speed at \(x=10\) \(\approx15.9\ \text{m s}^{-1}\); additional stopping distance \(\approx42.9\ \text{m}\)
Correct Answer
D
Correct Option:
Speed at \(x=10\) \(\approx15.9\ \text{m s}^{-1}\); additional stopping distance \(\approx42.9\ \text{m}\)

About This Question

This is Neco 2022 Further Mathematics Question 47. It is one of the objective questions from the 2022 Neco Further Mathematics examination.

Difficulty level: Hard .

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