At a given time in its flight $($ which we will designate as $t=0),$ an airplane is the $x_0=500m,y_0=1500m,$ and $z_0=2000m$; the velocity in each dimension is $v_{x,0}=100\frac{m}{s},v_{y,0}=200\frac{m}{s},$ and $v_{z,0}=5\mathrm{.}00\frac{m}{s}$; and the acceleration in each dimension is $a_{x,0}=15\mathrm{.}0\frac{m}{s^2},a_{y,0}=4\mathrm{.}00\frac{m}{s^2},$ and $a_{z,0}=1\mathrm{.}00\frac{m}{s^2}.$ What is its speed, new position, and distance traveled?