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

To solve the problem step by step, we will follow the principles of conservation of energy and analyze the given data.

### Step 1: Calculate the initial total energy
At time \( t \):
- Kinetic Energy (KE) = \( 30.0 \, J \)
- Potential Energy (PE) = \( 10.0 \, J \)

The total energy \( E \) at time \( t \) is given by:
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