Answer
$$\left( {\bf{a}} \right)v\left( t \right) = 22t + 4,\,\,\,\,\left( {\bf{b}} \right)v\left( 0 \right) = 0;\,\,\,\,\,\,\,\,v\left( 5 \right) = 114;\,\,\,\,\,\,v\left( {10} \right) = 224$$
Work Step by Step
$$\eqalign{
& {\text{let }}s\left( t \right) = 11{t^2} + 4t + 2 \cr
& \left( {\bf{a}} \right){\text{find the velocity using }}v\left( t \right) = s'\left( t \right).{\text{ then}}{\text{,}} \cr
& v\left( t \right) = s'\left( t \right) = {D_t}\left( {11{t^2} + 4t + 2} \right) \cr
& {\text{solve the derivatives using the power rule}} \cr
& v\left( t \right) = 11\left( {2t} \right) + 4\left( 1 \right) + 2 \cr
& v\left( t \right) = 22t + 4 \cr
& \cr
& \left( {\bf{b}} \right){\text{ evaluate the velocity }}v\left( t \right){\text{ at }}t = 0,{\text{ }}t = 5{\text{ and }}t = 10 \cr
& v\left( 0 \right) = 22\left( 0 \right) + 4 = 0 \cr
& v\left( 5 \right) = 22\left( 5 \right) + 4 = 114 \cr
& v\left( {10} \right) = 22\left( {10} \right) + 4 = 224 \cr} $$
