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# The indicated figure shows the path of a particle modeled by the vector-valued function$r(t)=\langle\pi t-\sin \pi t, 1-\cos \pi t\rangle .$The figure also shows the vectors $v(t) /\|v(t)\|$ and $a(t) /\|a(t)\|$ at the indicated values of t.Find $a_{T}$ and $a_{N}$ at $t=\frac{1}{2}, t=1$, and $t=\frac{3}{2}$.

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This is the first part of a two-part exercise, in which we are given the graph of the path of a particle defined with

$\bm{r}(t)= \langle \pi t-\sin\pi t, \,\, 1-\cos\pi t \rangle$

Our job is to find the components of acceleration $a_{T}$ and $a_{N}$ at points for which $t=1/2, t=1$ and $t=3/2.$

What are the tangential and normal components of acceleration, according to the corresponding theorem?

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