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Chapter 11: Q. 45 (page 872)

Use the given velocity vectors v(t)=r'(t)and initial positions in exercise to find the position function r(t).

Short Answer

Expert verified

r(t)=t22+3i+t23-4jis the required position function.

Step by step solution

01

Given Information

Consider vt=t,t2,r(0)=3,-4

The objective is to find the position function rt.

Since v(t)=r'(t)we have rt=鈭�v(t)dt

=鈭�t,t2dt=i鈭�tdt+j鈭�t2dt=t22i+t33j+c,

where cis a vector constant.

=t22+c1i+t33+c2j

Where c1and c2are scalars.

02

Calculation

Check: taking the derivative of r(t),t22+3i+t33-4jwe obtain r'(t)=ti+t2j,

which is the correct tangent vector function.

Next, we evaluate

r(0)=022+3i+033-4j=3i-4j=3,-4,

which is true according to the problem.

Thus r(t)=t22+3i+t33-4jis the required position function.

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