Answer
$${\bf{v}}\left( 1 \right) = {\bf{i}} + 5{\bf{j}} + 3{\bf{k}}$$$${\bf{a}}\left( 1 \right) = 0$$$${\text{speed}} = \sqrt {35} $$
Work Step by Step
$$\eqalign{
& {\bf{r}}\left( t \right) = t{\bf{i}} + 5t{\bf{j}} + 3t{\bf{k}},{\text{ }}t = 1 \cr
& \left( {\bf{a}} \right){\text{Find the vectors: }}{\bf{v}}\left( t \right),{\text{ }}{\bf{a}}\left( t \right){\text{ and speed}}{\text{.}} \cr
& {\bf{v}}\left( t \right) = {\bf{r}}'\left( t \right) \cr
& {\bf{v}}\left( t \right) = \frac{d}{{dt}}\left[ {t{\bf{i}} + 5t{\bf{j}} + 3t{\bf{k}}} \right] \cr
& {\bf{v}}\left( t \right) = {\bf{i}} + 5{\bf{j}} + 3{\bf{k}} \cr
& {\text{speed}} = \left\| {{\bf{v}}\left( t \right)} \right\| = \left\| {{\bf{i}} + 5{\bf{j}} + 3{\bf{k}}} \right\| \cr
& {\text{speed}} = \sqrt {1 + 25 + 9} = \sqrt {35} \cr
& {\bf{a}}\left( t \right) = {\bf{v}}'\left( t \right) \cr
& {\bf{a}}\left( t \right) = \frac{d}{{dt}}\left[ {{\bf{i}} + 5{\bf{j}} + 3{\bf{k}}} \right] \cr
& {\bf{a}}\left( t \right) = 0 \cr
& \cr
& \left( {\bf{b}} \right){\text{Evaluating }}{\bf{v}}\left( t \right),{\text{ }}{\bf{a}}\left( t \right){\text{ and speed at }}t = 1 \cr
& {\bf{v}}\left( 1 \right) = {\bf{i}} + 5{\bf{j}} + 3{\bf{k}} \cr
& {\text{speed}} = \sqrt {35} \cr
& {\bf{a}}\left( 1 \right) = 0 \cr} $$
