Chapter 12.6, Problem 34ES

The position function of a particle is given. Use theorem 12.6.3 to find

(a) the scalar tangential and normal components of acceleration at the stated time $t;$

(b) the vector tangential and normal components of acceleration at the stated time $t;$

(c) the curvature of the path at the point where the particle is located at the stated time $t.$

$\text{r}=e^t\cos t\text{i}+e^t\sin t\text{j;}t=\raisebox{1ex}{$\pi $}\!\left/ \!\raisebox{-1ex}{$4$}\right.$