Meriam, Kraige & Bolton — Kinematics of Particles: Problem 2_200

2/200 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 \(v, \mathbf{v}, a, \mathbf{a}, \mathbf{e}_t, \mathbf{e}_n, a_t, \mathbf{a}_t, a_n, \mathbf{a}_n, \rho\), and \(\dot{\beta}\) (the angular velocity of the normal to the path) when \(t = 3.25\text{ s}\). Express all vectors in terms of the unit vectors \(\mathbf{i}\) and \(\mathbf{j}\).