Problem $6\mathrm{.}3.$ Suppose the path $of$ a point particle $is$ traced $by$ the curve $$:$[0,5]R^{3}by$

$(t)=($:$t^2,\frac{1}{2}sin(\sqrt[\phantom{2}]{21}{t}^2),\frac{1}{2}cos(\sqrt[\phantom{2}]{21}{t}^2)$:$).(0)$ and its position $at$ time $tis(t)$ for $0t5t$ and find the velocity vector

and speed $att=2.$

Problem $6\mathrm{.}4.$ Suppose the path $of$ a point particle $is$ traced $by$ the curve $$:$[0,100]R^{2}by$

$(t)=($:$\frac{6t}{1+t^3},\frac{6t^2}{1+t^3}$:$).(0)$ and it's position $at$ time $tis(t)$ for $0t100t$ and find the velocity vector

and speed $att=1.$