Answer
$$\left( {\bf{a}} \right)v\left( t \right) = 36t - 13,\,\,\,\,\left( {\bf{b}} \right)v\left( 0 \right) = - 13;\,\,\,\,\,\,\,\,v\left( 5 \right) = 167;\,\,\,\,\,\,v\left( {10} \right) = 347$$
Work Step by Step
$$\eqalign{
& {\text{let }}s\left( t \right) = 18{t^2} - 13t + 8 \cr
& \left( {\bf{a}} \right){\text{find the velocity using }}v\left( t \right) = s'\left( t \right).{\text{ then}}{\text{,}} \cr
& v\left( t \right) = s'\left( t \right) = {D_t}\left( {18{t^2} - 13t + 8} \right) \cr
& {\text{solve the derivatives using the power rule}} \cr
& v\left( t \right) = 18\left( {2t} \right) - 13\left( 1 \right) + 0 \cr
& v\left( t \right) = 36t - 13 \cr
& \cr
& \left( {\bf{b}} \right){\text{ evaluate the velocity }}v\left( t \right){\text{ at }}t = 0,{\text{ }}t = 5{\text{ and }}t = 10 \cr
& v\left( 0 \right) = 36\left( 0 \right) - 13 = - 13 \cr
& v\left( 5 \right) = 36\left( 5 \right) - 13 = 167 \cr
& v\left( {10} \right) = 36\left( {10} \right) - 13 = 347 \cr} $$
