   Chapter 12.3, Problem 23E

Chapter
Section
Textbook Problem

# Finding a Position Vector by IntegrationIn Exercises 21-26, use the given acceleration vector and initial conditions to find the velocity and position vectors. Then find the position at time t = 2 . a ( t ) = − cos t i − sin t j , v ( 0 ) = j + k , r ( 0 ) = 1

To determine

To calculate: The velocity and position vector at t=0, position vector at t=2 for given acceleration vector a(t)=costi^sintj^.

Explanation

Given:

The given acceleration vector is and initial conditions a(t)=costi^sintj^; v(o)=j^+k^, r(o)=i^

Formula used:

The integrations formula is:

v(t)=a(t)dtr(t)=v(t)dt

Calculation:

The velocity vector is v(t)=a(t)dt=(costi^sintj^)dt

=sinti^+costj^+cwhere c=c1i^+c2j^+c3k^applying the condition v(o)=j^+k^; we getv(o)=tj^+c1i^+c2j^+c3k^=j^+k^ c1i^+(c2+2)j^+(c31)k^=o&#

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