Final answer:
The work done on an object moving from (3 m, 4 m) to (6 m, 8 m) under a force of 3i + 4j is calculated using the dot product of the force and displacement vectors, resulting in 25 Joules of work done.
Step-by-step explanation:
To calculate the work done on an object by a force during its displacement, we can use the dot product of the force vector and the displacement vector.
In this case, the force vector is F = 3i + 4j (in Newtons) and the displacement vector can be found by subtracting the initial position vector (x1, y1) from the final position vector (x2, y2), which gives D = (x2 - x1)i + (y2 - y1)j (in meters).
The work done, W, is then calculated as:
W = F · D
W = (3)(x2 - x1) + (4)(y2 - y1)
Substituting the given values for an example where the object moves from (3 m, 4 m) to (6 m, 8 m):
W = 3(6 - 3) + 4(8 - 4) = 3(3) + 4(4) = 9 + 16 = 25 Joules
Therefore, the work done by the force as the object moves from (3 m, 4 m) to (6 m, 8 m) is 25 Joules.