A particle is moving in the x - y plane with an initial kinetic energy of 20 J . A constant force F = (3 i + 4 j ) N acts on the particle as it moves from the coordinates (1 m , 2 m ) to (3 m , -1 m ) . The kinetic energy of the particle at

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A particle is moving in the x - y plane with an initial kinetic energy of 20 J . A constant force F = (3 i + 4 j ) N acts on the particle as it moves from the coordinates (1 m , 2 m ) to (3 m , -1 m ) . The kinetic energy of the particle at the final position is:

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Correct answer: A. 14 J

Initial position vector r _i = i + 2 j Final position vector r _f = 3 i - j Displacement vector r = r _f - r _i = (3 - 1) i + (-1 - 2) j = 2 i - 3 j Work done by the constant force W = F r = (3 i + 4 j ) (2 i - 3 j ) W = (3)(2) + (4)(-3) = 6 - 12 = -6 J Using the work-energy theorem, W = K_f - K_i -6 = K_f - 20 K_f = 14 J Answer: 14 J

A particle is moving in the x - y plane with an initial kinetic energy of 20 J . A constant force F = (3 i + 4 j ) N acts on the particle as it moves from the coordinates (1 m , 2 m ) to (3 m , -1 m ) . The kinetic energy of the particle at the final position is:

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