Tofind: the position of the particle through the given velocity.

Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

Solutions

Chapter 4, Problem 58RE
To determine

Tofind:the position of the particle through the given velocity.

Expert Solution

Theposition of the particle is s(t)=-sint-3cost+3t+3.

Explanation of Solution

Given:

a(t)=sint+3cost,  s(0)=0, v(0)=2.

Concept used:

Antiderivative=integration

f(t)dt=f(t) . Or dydtdt=y .

Since, the multiplication of two operators ×ddt=1 .

Integration formula:

xndx=xn+1n+1 .

Calculation:

a(t)=sint+3cost,  s(0)=0, v(0)=2. .

a(t)=sint+3cost .

a(t)dt=(sint+3cost)dt

a(t)dt=v(t)=-cost+3sint+C1 .

v(t)=-cost+3sint+C1 .

v(0)=-cost+3sint+C1 .

2=-cos0+3sin0+C1 .

C1=3.

v(t)=-cost+3sint+3.

v(t)dt=s(t)=-sint-3cost+3t.

s(t)=-sint-3cost+3t+C2

s(0)=-sin0-3cos0+3(0)+C2

C2=3.

s(t)=-sint-3cost+3t+3.

Hence the position of the particle is s(t)=-sint-3cost+3t+3.

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