## Related questions with answers

The position vector r describes the path of an object moving in space. (b) Evaluate the velocity vector and acceleration vector of the object at the given value of Position Vector: r(t) = ⟨cos³ t, sin³ t, 3t⟩ Time: t = π

Solutions

Verified$\begin{align*} &\vec{v}(t) = <\;-3 \cos^2 t \sin t,3 \sin^2 t \cos t, 3\;>\\ &|| \vec{v}(t) || = 3\sqrt{\cos^2t \sin^2t + 1}\\ &\vec{a}(t) = <\;-3\cos t(\cos^2 t -2\sin^2t) ,3\sin t(2\cos^2t - sin^2t), 0\;> \end{align*}$

From part A we have the velocity vector, speed, and acceleration (to the left).

From the part $a$ of this exercise, we obtained the following **vector functions**</span>:

$\begin{align*} \textbf{velocity}&=\textbf{v}(t)= \langle-3\cos^2t\sin t, 3\sin^2t\cos t, 3 \rangle \\ \textbf{acceleration}&=\textbf{a}(t)= \langle3\cos t(2\sin^2 t-\cos^2 t) ,3\sin t(2\cos^2-\sin^2 t) ,0\rangle. \\ \end{align*}$

In this problem, we want to evaluate the obtained **velocity vector** and **acceleration vector**</span> at $t=\pi$.

*What method should we use to evaluate the vector functions?*

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