Parametric Motion and Arc Length

A student studies a particle’s motion along a circle given by $x(t)=\cos(t)$, $y(t)=\sin(t)$ for $0\le t\le 2\pi$, whose arc length is $2\pi$. What would happen if the particle’s speed is doubled by defining $x(t)=\cos(2*t)$ and $y(t)=\sin(2*t)$; how does this affect the total arc length traced over the same time interval?