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Calculus (MindTap Course List)

8th Edition
James Stewart
ISBN: 9781285740621

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Calculus (MindTap Course List)

8th Edition
James Stewart
ISBN: 9781285740621
Textbook Problem

A particle is moving according to the given data. Find the position of the particle.

v ( t ) = 2 t sin t ,     s ( 0 ) = 3

To determine

To find:

The position of the particle s(t)

Solution:st=t2+cost+2

Explanation

1) Concept:

i. Position is antiderivative of velocity.

ii. If F is an antiderivative of f on an interval I, then the most general antiderivative of f on I is Fx+c where c is an arbitrary constant.

2) Formula:

sinx=ddx-cosx

3) Given:

vt=2t-sint,  s0=3

4) Calculations:

Letst be the position function.

A particle is moving with a velocity of vt=2t-sint and s0=3

The general antiderivative of vt usingrules of antiderivative

st=2*t22-(-cost)+C where C is the arbitrary constant

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