Final answer:
The work done by the force is 9.6J.
Step-by-step explanation:
To calculate the work done by a force, you need to multiply the force by the distance it acts over. In this case, the force is given by F₁ = (3N)i + (4N)j, and the particle moves from x = 2.3m to x = 5.5m. To find the work done, you need to calculate the displacement, which is the difference in x-coordinates, and then multiply it by the force:
Displacement (Δx) = 5.5m - 2.3m = 3.2m
Work (W) = Force (F₁) × Displacement (Δx)
Substituting the values, W = (3N)(3.2m) = 9.6J
Therefore, the work done by the force on the particle as it moves from x = 2.3m to x = 5.5m is 9.6J.