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Object is moving on straight line of equation 3x+4y+5=0 and force acting of object f=3i+4j then find work done when it move from (x1, y1) to (x2,y2)​

User Zouzias
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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.

User Dgel
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