Meriam, Kraige & Bolton — Kinematics of Particles: Problem 2_117

2/117 The slider P can be moved inward by means of the string S, while the slotted arm rotates about point O. The angular position of the arm is given by \(\theta = 0.8t - \frac{t^2}{20}\), where \(\theta\) is in radians and \(t\) is in seconds. The slider is at \(r = 1.6 \text{ m}\) when \(t = 0\) and thereafter is drawn inward at the constant rate of \(0.2 \text{ m/s}\). Determine the magnitude and direction (expressed by the angle \(\alpha\) relative to the \(x\)-axis) of the velocity and acceleration of the slider when \(t = 4 \text{ s}\).