Meriam, Kraige & Bolton — Kinematics of Particles: Problem 2_201

2/201 The coordinates of a particle which moves with curvilinear motion are given by \(x = 10.25t + 1.75t^2 - 0.45t^3\) and \(y = 6.32 + 14.65t - 2.48t^2\), where \(x\) and \(y\) are in millimeters and the time \(t\) is in seconds. Determine the values of \(v, \mathbf{v}, a, \mathbf{a}, \mathbf{e}_r, \mathbf{e}_\theta, v_r, \mathbf{v}_r, v_\theta, \mathbf{v}_\theta, a_r, \mathbf{a}_r, a_\theta, \mathbf{a}_\theta, r, \dot{r}, \ddot{r}, \theta, \dot{\theta}\), and \(\ddot{\theta}\) when \(t = 3.25\text{ s}\). Express all vectors in terms of the unit vectors \(\mathbf{i}\) and \(\mathbf{j}\). Take the \(r\)-coordinate to proceed from the origin, and take \(\theta\) to be measured positive counterclockwise from the positive \(x\)-axis.