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?