Let S1 = frame of reference at rest.
S2 = frame of reference at constant velocity
S3 = frame of reference at constant acceleration
S4 = frame of reference at uniform circular motion
A block A is at rest as seen from frame of reference S1
`{:("Column I",,,"Column II"),((A)S1,,,(P)SigmaFne0),((B)S2,,,(Q)SigmaF=0),((C)S3,,,(R)a=0),((D)S4,,,(S)ane0),(,,,(T)F_("psuedo")=0):}`
Where `SigmaF` is the resultant force and a is the acceleration of the body.

Answer

To solve the problem, we need to analyze the four frames of reference (S1, S2, S3, S4) and determine the corresponding values for the resultant force (ΣF), acceleration (a), and pseudo force (F_pseudo) for each frame.

### Step-by-Step Solution:

1. **Frame S1 (At Rest)**
- Since block A is at rest in frame S1, the resultant force acting on it must be zero (ΣF = 0).
- The acceleration of block A is also zero (a = 0) because it is at rest.
- Since S1 is an inertial frame, there is no pseudo force acting on block A (F_pseudo = 0).
- **Conclusion for S1**:
- ΣF = 0 (P)
- a = 0 (R)
- F_pseudo = 0 (T)

2. **Frame S2 (Constant Velocity)**
- In frame S2, which is moving at a constant velocity, block A appears to be at rest (relative motion).
- The resultant force acting on block A is still zero (ΣF = 0).
- The acceleration of block A remains zero (a = 0) since it is not accelerating in this frame.
- As S2 is also an inertial frame, there is no pseudo force acting on block A (F_pseudo = 0).
- **Conclusion for S2**:
- ΣF = 0 (P)
- a = 0 (R)
- F_pseudo = 0 (T)

3. **Frame S3 (Constant Acceleration)**
- In frame S3, which is accelerating, the observer will see block A as if it is moving in the opposite direction due to the acceleration of the frame.
- The resultant force acting on block A remains zero (ΣF = 0) because it is at rest in its own frame.
- However, since the frame is accelerating, the observer will perceive a pseudo force acting on block A in the opposite direction of the frame's acceleration (F_pseudo ≠ 0).
- The acceleration of block A is not zero in this frame because it appears to be moving in the opposite direction (a ≠ 0).
- **Conclusion for S3**:
- ΣF = 0 (P)
- a ≠ 0 (S)
- F_pseudo ≠ 0 (not explicitly stated but inferred)

4. **Frame S4 (Uniform Circular Motion)**
- In frame S4, which is in uniform circular motion, the observer will see block A as if it is experiencing an outward pseudo force due to the circular motion.
- The resultant force acting on block A is not zero (ΣF ≠ 0) because it is undergoing centripetal acceleration.
- The acceleration of block A is not zero (a ≠ 0) because it is in circular motion.
- There is a pseudo force acting on block A due to the non-inertial nature of the frame (F_pseudo ≠ 0).
- **Conclusion for S4**:
- ΣF ≠ 0 (not stated but inferred)
- a ≠ 0 (not stated but inferred)
- F_pseudo ≠ 0 (not stated but inferred)

### Final Matching:
- For S1: (P, R, T)
- For S2: (P, R, T)
- For S3: (P, S, not stated)
- For S4: (not stated, not stated, not stated)