Final answer:
The question addresses the kinematics of a constrained particle, focusing on determining the angular velocity and net force, among other parameters. Angular velocity relates linear velocity to the circular path radius, while net force involves mass and acceleration as per Newton's second law.
Step-by-step explanation:
Kinematics of a Constrained Particle
The question involves a scenario where the end points of bar AB are moving along certain paths. Given that point A has a velocity of 8 ft/s and an acceleration of 3 ft/s², several kinematic quantities are to be determined including the angular velocity and net force acting on the particle. Although the fundamental theorem of calculus is mentioned, the information provided doesn't include an integral or function to be integrated, so we cannot apply it directly here.
To find the angular velocity, we would generally relate the linear velocity to the radius of the circular path, using the equation angular velocity (\(\omega\)) = linear velocity (v) / radius (r). The kinematics of point A involve analyzing its motion, which includes both the linear displacement and the acceleration affecting it over time.
The net force acting on point A can be found using Newton's second law, where the net force is equal to the mass of the object multiplied by its acceleration (F = ma). However, to calculate the actual force, we would need to know the mass of the object.