Let r(t) is the position vector for a particle in space at time t. Find the particle's velocity andacceleration. Hence find the speed and the direction of motion for the

given value of t. \begin{array}{l} \text { a. }\\ \mathbf{r}(t)=2 \cos t \mathbf{i}+2 \sin t \mathbf{j}+t \mathbf{k}, \quad \boldsymbol{t}=\frac{1}{4} \pi \end{array} \text { b. } \quad \mathbf{r}(t)=2 t \mathbf{i}+3 \operatorname{In} t \mathbf{j}+e^{2 t} \mathbf{k}, t=\mathbf{1}