The equations x$($t$)=10$etsin$($t$)$and$$y$($t$)=10$etcos$($t$)$x$($t$)=10$etsin$($t$)$and$$y$($t$)=10$etcos$($t$)$ give the position of a particle at each time tt from t$=0$to$$t$=$t$=0$to$$t$=$$.$ Find the initial speed of the particle, the terminal speed, and the distance traveled.