91Ó°ÊÓ

A particle travels along the path of a helix with the equation \(\mathbf{r}(t)=\cos (t) \mathbf{i}+\sin (t) \mathbf{j}+t \mathbf{k} .\) See the graph presented here: Find the following: Speed of the particle at any time

A particle travels along the path of a helix with the equation \(\mathbf{r}(t)=\cos (t) \mathbf{i}+\sin (t) \mathbf{j}+t \mathbf{k} .\) See the graph presented here: Find the following: Acceleration of the particle at any time

A particle travels along the path of a helix with the equation \(\mathbf{r}(t)=\cos (t) \mathbf{i}+\sin (t) \mathbf{j}+t \mathbf{k} .\) See the graph presented here: Find the following: Find the unit tangent vector for the helix.

A particle travels along the path of an ellipse with the equation \(\mathbf{r}(t)=\cos t \mathbf{i}+2 \sin t \mathbf{j}+0 \mathbf{k}\). Find the following: Velocity of the particle

A particle travels along the path of an ellipse with the equation \(\mathbf{r}(t)=\cos t \mathbf{i}+2 \sin t \mathbf{j}+0 \mathbf{k}\). Find the following: Speed of the particle at \(t=\frac{\pi}{4}\)

A particle travels along the path of an ellipse with the equation \(\mathbf{r}(t)=\cos t \mathbf{i}+2 \sin t \mathbf{j}+0 \mathbf{k}\). Find the following: Acceleration of the particle at \(t=\frac{\pi}{4}\)

Given \(\quad\) the vector-valued function \(\mathbf{r}(t)=\langle\tan t, \sec t, 0\rangle\) (graph is shown here), find the following: Velocity

Given \(\quad\) the vector-valued function \(\mathbf{r}(t)=\langle\tan t, \sec t, 0\rangle\) (graph is shown here), find the following: Speed

Given \(\quad\) the vector-valued function \(\mathbf{r}(t)=\langle\tan t, \sec t, 0\rangle\) (graph is shown here), find the following: Acceleration

Given \(\quad\) the vector-valued function \(\mathbf{r}(t)=\langle\tan t, \sec t, 0\rangle\) (graph is shown here), find the following: Find the minimum speed of a particle traveling along the curve \(\mathbf{r}(t)=\langle t+\cos t, t-\sin t\rangle \quad t \in[0,2 \pi)\).