A particle of mass 2 kg, initially at rest at the origin, is subjected to a constant force F = (4 i + c j + 2 k ) N. It reaches a position vector r = (2 i - 3 j + k ) m with a speed of 5 m/s. The value of the unknown component c is:

Step-by-step solution

According to the Work-Energy Theorem, the total work done on the particle equals its change in kinetic energy: W = K = 1 2 mv^2 - 1 2 mu^2 Given m = 2 kg, v = 5 m/s, and u = 0 m/s: W = 1 2 (2)(5)^2 - 0 = 25 J The work done by the constant force is also given by the dot product of the force and the displacement vector. Since the particle starts at the origin, the displacement vector is simply the final position vector r . W = F r W = (4 i + c j + 2 k ) (2 i - 3 j + k ) W = (4)(2) + (c)(-3) + (2)(1) W = 8 - 3c + 2 W