(Instantaneous power and kinetic energy)
Answer the following questions with proper reasoning and mathematical steps wherever required.
a. (i) Define instantaneous power for a mechanical system.
b. (ii) Starting from suitable basic relations, establish that the instantaneous power delivered to a particle equals the time-rate of change of its kinetic energy, that is, P=dtdK.
c. (iii) Explain why the equality obtained in part (ii) holds even when the force acting on the particle varies with time as well as with position.