The trajectory of a particle in a plane as a function of the time \(t\) in seconds is given by the parametric equations \begin{equation*} x=3t^2+2t-3, \ \ y=2t^3+2\text{.} \end{equation*} Prove that ...

An object is moving counter-clockwise along a circle with the centre at the origin. At \(t=0\) the object is at point \(A(0,5)\) and at \(t=2\pi\) it is back to point \(A\) for the first time.