Final answer:
The change in kinetic energy (KE) of the particle as it moves from point (2, 3) to (3, 0) under the force F=(3x2i+4j) N is computed using the work-energy principle. The total work done, exclusively due to the variable component of the force in the x-direction, is 19 J. Thus, the particle's change in kinetic energy is 19 J, and the correct answer is D. 19J.
Step-by-step explanation:
To calculate the change in kinetic energy of the particle as it moves from point (2, 3) to (3, 0), we need to determine the work done by the force F=(3x2i+4j) N on the particle as it makes this transition. The work done by a force on an object is given by the line integral of the force along the path of the object. In this case, we can simplify things since the force in the direction of j is constant, and only the i component of the force depends on x. Therefore, we can solve for the work done by the force in the x-direction.
Let's calculate the change in kinetic energy (KE) of the particle. The work-energy principle states that the work done on a particle is equal to the change in its kinetic energy. The work done on the particle as it moves in the x-direction from x = 2 to x = 3 is the integral of the x-component of the force F with respect to x:
W = ∫23 3x2 dx = [x3]23 = 33 - 23 = 27 - 8 = 19 J
The work done by the y-component is zero because there is no movement in the y-direction, so the total work done is 19 J. This means that the change in kinetic energy of the particle, as it moves from (2, 3) to (3, 0), is 19 J. Therefore, the correct answer is D. 19J.