Chapter 3.2, Problem 66E

Find the velocity and the speed of a panicle with the position function $r\left(t\right)=\frac{\left(2t-1\right)}{\left(2t+1\right)}i+\ln \left(1-4t^2\right)j$ . The speed of a particle is the magnitude of the velocity and is represented by $\Vert r\text{'}\left(t\right)\Vert$ .

A particle moves on a Circular path of radius b according to the function $\text{r}\left(t\right)=b\cos \left(\omega t\right)\text{i}+b\sin \left(\omega t\right)\text{j}$ , where $\omega$ is the angular velocity, $d\theta /dt$ .