A point P moving on the coordinate plane has position $( x , y )$ at time $t$ $(t > 0)$ given by $$x = t - \frac { 2 } { t } , \quad y = 2 t + \frac { 1 } { t }$$ What is the speed of point P at time $t = 1$? [3 points]
(1) $2 \sqrt { 2 }$
(2) 3
(3) $\sqrt { 10 }$
(4) $\sqrt { 11 }$
(5) $2 \sqrt { 3 }$

A particle is moving along the $x$-axis with its coordinate with time $t$ given by $x ( t ) = 10 + 8 t - 3 t ^ { 2 }$. Another particle is moving along the $y$-axis with its coordinate as a function of time given by $y ( t ) = 5 - 8 t ^ { 3 }$. At $t = 1 \mathrm {~s}$, the speed of the second particle as measured in the frame of the first particle is given as $\sqrt { v }$. Then $v$ (in $\mathrm { m s } ^ { - 1 }$) is $\_\_\_\_$.