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## Homework Statement

A particle moves with position function r(t) = t lnt[tex]\hat{i}[/tex] + t[tex]\hat{j}[/tex] + e

^{-t}[tex]\hat{k}[/tex]

Find the velocity vector, speed, and acceleration.

## Homework Equations

## The Attempt at a Solution

[tex]\hat{v}[/tex](t) = (1 + lnt)[tex]\hat{i}[/tex] + [tex]\hat{j}[/tex] - e

^{-t}[tex]\hat{k}[/tex]

[tex]\hat{a}[/tex](t) = 1/t [tex]\hat{}i[/tex] + e

^{-t}[tex]\hat{k}[/tex]

[tex]\left\|[/tex]v(t)[tex]\right\|[/tex] = [tex]\sqrt{lnt + e^(-2t) + 2lnt + 2}[/tex]

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