A particle moves in the xyxyxy-plane such that x(t)=∫0tcos(u2) dux(t) = \int_0^t \cos(u^2) \, dux(t)=∫0tcos(u2)du and y(t)=∫0tsin(u2) duy(t) = \int_0^t \sin(u^2) \, duy(t)=∫0tsin(u2)du. What is the speed v(t)=(x′(t))2+(y′(t))2v(t) = \sqrt{(x'(t))^2 + (y'(t))^2}v(t)=(x′(t))2+(y′(t))2?
111
ttt
2cos(t2)\sqrt{2} \cos(t^2)2cos(t2)
t2t^2t2