Problem 1.26

A point moves in the plane \(x y\) according to the law \(x\) \(=a \sin \omega t, y=a(1-\cos \omega t),\) where \(a\) and \(\omega\) are positive constants. Find: (a) the distance \(s\) traversed by the point during the time \(\tau\); (b) the angle between the point's velocity and acceleration vectors.