Serway & Jewett — Motion in Two Dimensions: Problem 2

The coordinates of an object moving in the \(xy\) plane vary with time according to the equations \(x = -5.00 \sin \omega t\) and \(y = 4.00 - 5.00 \cos \omega t\), where \(\omega\) is a constant, \(x\) and \(y\) are in meters, and \(t\) is in seconds. (a) Determine the components of velocity of the object at \(t = 0\). (b) Determine the components of acceleration of the object at \(t = 0\). (c) Write expressions for the position vector, the velocity vector, and the acceleration vector of the object at any time \(t > 0\). (d) Describe the path of the object in an \(xy\) plot.