An object with an initial kinetic energy of 20 J is subjected to a constant force F = (4 i - 3 j ) N . Under the influence of this force, the object undergoes a displacement r = (6 i + 8 j ) m . The kinetic energy of the object at the end of this displacement is

Step-by-step solution

According to the work-energy theorem, the net work done on an object equals its change in kinetic energy: W = K_f - K_i . The work done by the constant force is given by the dot product of the force and displacement vectors: W = F r = (4 i - 3 j ) (6 i + 8 j ) W = (4)(6) + (-3)(8) = 24 - 24 = 0 J Since the force and displacement vectors are orthogonal, the work done is zero. Using the work-energy theorem: 0 = K_f - 20 K_f = 20 J The kinetic energy of the object remains unchanged. Answer: 20 J