   Chapter 12.3, Problem 19E

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 ) = i + j + k , v ( 0 ) = 0 , r ( 0 ) = 0

To determine

To calculate: The velocity and position vector at t=0, position vector at t=2 for given acceleration vector a(t)=i^+j^+k^.

Explanation

Given:

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

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 = (i^+j^+k^) dt = ti^+tj^+tk^+cwhere c=c1i^+c2j^+c3k^Applying the condition v(o)=o, we getv(o) = c1i^+c2j^+c3k^=o c1=c2=c3so, the velocity at any time t is v(t) = ti^+tj^+tk^By integrating, we get r(t) = v(t)dt=

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