This problem is an application for the "Parametric Equation" topic. An object moves in a plane and its location at a time $t($in second$)$ is given by the parametric equation $x=\frac{1}{\sqrt[\phantom{2}]{t+1}}$ and $y=\frac{2}{\sqrt[\phantom{2}]{t+1}}($inches$)$

The speed the object at a time is given by $\sqrt[\phantom{2}]{(x^{\text{'}}{)}^2+(y^{\text{'}}{)}^2}.$ Find the speed of the object at the time $t=3.$

Find the length of the trajectory curve $($the total distance the object is moving$)$ between $0t3.$