Meriam, Kraige & Bolton — Kinematics of Particles: Problem 2_161

2/161 For the cars of Prob. 2/160, determine the instantaneous values of \(\ddot{r}\) and \(\ddot{\theta}\) if car A is slowing down at a rate of \(1.25 \text{ m/s}^2\) and car B is speeding up at a rate of \(2.5 \text{ m/s}^2\). Refer to the printed answers for Prob. 2/160 as needed. Context from Problem 2/160: Car B has a speed of \(30 \text{ km/h}\) and car A has a speed of \(40 \text{ km/h}\). Both are moving on concentric circular paths. The radius of the path for car A is \(R_A = 75 \text{ m}\) and for car B is \(R_B = 105 \text{ m}\). At the instant shown, the radius from the center of curvature to car B makes an angle of \(30^\circ\) with a horizontal reference, and the radius to car A makes an angle of \(45^\circ\) with the same reference. Both cars are moving counter-clockwise.