At time `t`, the kinetic energy of a particle is `30.0J` and the potential energy of the system to which it belongs is `10.0J`. At some later time `t_f`, the kinetic energy of the particle is `18J`, what are the potential energy and the total energy at time `t_f`? If the potential energy of the system at time `t_3` is `5.00J`, are any non-conservative forces acting on the particle? Explain.

Explanation

a. `U_f=K_i-K_f+U_i=30.0-18.0+10.0=22.0J`
`E=U_i+K_i=40.0J`
b. Yes, `DeltaE_(mech)=DeltaK+DeltaU` is not equal to zero, some non-conservative forces must act. For conservative forces, `DeltaK+DeltaU=0`.