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A particle is moving with the given data. Find the position of the particle.

$ a(t) = 2t + 1 $, $ \quad s(0) = 3 $, $ \quad v(0) = -2 $

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01:37

Wen Zheng

01:32

Amrita Bhasin

Calculus 1 / AB

Calculus 2 / BC

Chapter 4

Applications of Differentiation

Section 9

Antiderivatives

Derivatives

Differentiation

Volume

Missouri State University

Baylor University

University of Nottingham

Lectures

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In mathematics, the volume of a solid object is the amount of three-dimensional space enclosed by the boundaries of the object. The volume of a solid of revolution (such as a sphere or cylinder) is calculated by multiplying the area of the base by the height of the solid.

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A review is a form of evaluation, analysis, and judgment of a body of work, such as a book, movie, album, play, software application, video game, or scientific research. Reviews may be used to assess the value of a resource, or to provide a summary of the content of the resource, or to judge the importance of the resource.

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So we're giving a particle with the following data acceleration that's a F. T equals two T plus one. So when we find its velocity velocity is going to be the anti derivative of acceleration. So it's going to be um t squared plus T. And then we're gonna have plus a constant. But we know that via zero is negative two. That means this is gonna be minus two. Our position function at safety, it's going to be able to t cube over three. Okay. Plus t squared over two and then we're going to have minus two T. And um plus a constant. But we know that s of zero is three. So that means our constant value is three. Therefore this is our final position function.

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