If $\displaystyle r(t) = <t^2, 3t, e^t>$, find the tangential and normal components of the acceleration vector.

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- May 22nd 2008, 04:47 AMkenshinofkinTangential and normal components
If $\displaystyle r(t) = <t^2, 3t, e^t>$, find the tangential and normal components of the acceleration vector.

- May 22nd 2008, 05:26 AMkenshinofkin
This is what I have so far

$\displaystyle a(t) = r"(t) = <2, 0, e^t>$

$\displaystyle T = r'(t)/||r'|| = <2t,3,e^t>/(4t^2 + 9 + e^t^2) = ?$

Am I on the right track? My algebra is a rusty. Can I do anything with T. - May 22nd 2008, 03:23 PMkenshinofkin
There was an error let me try this again.

$\displaystyle

T = r'(t)/||r'|| = <2t,3,e^t>/(4t^2 + 9 + (e^t)^2)^(1/2)

$

So am I on the right track? How can i reduce T? The next step is to find N then do a dot T and a dot N correct? - May 22nd 2008, 05:16 PMkenshinofkin
Anyone out there that can help please!