Meriam, Kraige & Bolton — Kinetics of Particles: Problem 3_159

3/159 All elements of the previous problem remain unchanged, except that the force \( P \) is now held at a constant 30° angle relative to the horizontal. Determine the time \( t_s \) at which the initially stationary 20-kg block comes to rest. [From Problem 3/158: The initially stationary 20-kg block is subjected to the time-varying horizontal force whose magnitude \( P \) is shown in the plot. Note that the force is zero for all times greater than 3 s. Initial velocity \( v_0 = 0 \). Friction coefficients: \( \mu_s = 0.60 \), \( \mu_k = 0.40 \). From the plot, \( P \) increases linearly from 0 to 150 N over 3 seconds, so \( P = 50t \) for \( 0 \leq t \leq 3 \) s.]