A particle of mass \(m\) moves in a horizontal circular path of radius \(R\) on a frictionless surface. The particle speeds up over time such that its tangential speed \(v(t)\) increases continuously. At a given instant, the net force acting on the particle has a radial component of magnitude \(F_{\text{rad}}\) directed toward the center of the path and a tangential component of magnitude \(F_{\text{tan}}\) in the direction of motion. Which of the following correctly identifies the instantaneous power \(P_{\text{rad}}\) delivered to the particle by the radial component and correctly relates the instantaneous power \(P_{\text{tan}}\) delivered by the tangential component to the total instantaneous power \(P_{\text{net}}\) delivered to the particle?