Final answer:
The questions involve calculating work done, finding velocity, and determining other forces and physical quantities using principles like the work-energy theorem and Newton's laws of motion.
Step-by-step explanation:
The question is asking us to calculate the work done by force F1 on a particle as it moves along a defined path in Cartesian coordinates, and in other scenarios, it involves finding various physical quantities such as velocity, acceleration, and the resultant force on particles under the influence of certain forces.
To calculate work done by a constant force, the formula is Work = Force × Displacement × cos(θ), where θ is the angle between the force and displacement vectors. For a force that depends on position, the work done is calculated by integrating the force over the path of motion. To find a third force, we apply Newton's second law and the condition that the total force is the vector sum of all individual forces. When computing velocity or speed at different positions, we employ the work-energy theorem, which equates work done to the change in kinetic energy (½mv2).