1. Non-uniform rod equilibrium: Calculate the center of mass position given the forces acting on the rod.
2. Particle collision: Determine the speed of particle P post-collision, its direction of motion, and the coefficient of friction between Q and the plane.
3. Car deceleration: Find the speed of a car as it reaches a road sign under uniform deceleration, then calculate the time to reach the sign under different deceleration scenarios.
4. Particle position vector: Calculate the angle between the particle′s position vector and the vertical vector at a given time and determine the distance from the origin.
5. Friction on bead: Calculate the friction force acting on a bead on a rough wire, and determine the coefficient of friction using given constraints.
6. Ship velocity and position: Find the velocity of a ship, the position vector after a given time, the position vector of a lighthouse, and when the ship is due south of it.