- #1

scoobiedoober

- 7

- 0

## Homework Statement

I was following through the notes I took in my Calc class, and either I wrote down the formulas incorrectly, my professor did this problem incorrectly, or I wrote the answer down incorrectly. I'm just going to redo it here, so could someone give me a thumbs up or thumbs down if I did it correctly? Thanks.

Problem:

Find the tangential component of the acceleration vector of the given partial motion vector:

[tex]r(t)=\langle e^{-t},\sqrt{2}t,e^t\rangle[/tex]

## Homework Equations

[tex]a_T=\frac{d}{dt}|v|[/tex]

## The Attempt at a Solution

[tex]v(t)=\frac{dr(t)}{dt}=\langle -e^{-t},\sqrt{2},e^t \rangle[/tex]

[tex]|v|=\sqrt{e^{-2t}+2+e^{2t}}[/tex]

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

[tex]|v|=e^{-t}+e^t[/tex]

[tex]a_T=\frac{d}{dt}|v|=-e^{-t}+e^t[/tex]