   Chapter 4.9, Problem 63E ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

#### Solutions

Chapter
Section ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

# A particle is moving with the given data. Find the position of the particle.a(t) = 10 sin t + 3 cos t, s(0) = 0, s(2π) = 12

To determine

To find: The position of particle.

Explanation

Given data:

a(t)=10sint+3cost , s(0)=0 and s(2π)=12 .

Formula Used:

Write the expression for acceleration function a(t) .

a(t)=v(t) (1)

Here,

v(t) is first derivative of velocity function v(t) .

Write the expression for velocity function v(t) .

v(t)=s(t) (2)

Here,

s(t) is first derivative of position function s(t) .

Antiderivative of cost is sint , sint is cost and 1 is t .

Calculation:

Substitute 10sint+3cost for a(t) in equation (1),

v(t)=10sint+3cost

Antiderivate the expression with respect to t,

v(t)=10(cost)+3(sint)+C=10cost+3sint+C

Here,

C is arbitrary constant.

Substitute 10cost+3sint+C for v(t) in equation (2),

s(t)=10cost+3sint+C

Antiderivate the expression with respect to t,

s(t)=10(sint)+3(cost)+Ct+D

s(t)=10sint3cost+Ct+D (3)

Here,

D is arbitrary constant

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