(A): Velocity-time graph for an object in uniform motion along a straight path is a straight line parallel to the time axis.
(R ):In uniform motion of an object velocity increases as the square of time elapsed.

Answer

To analyze the statements given in the question, we will evaluate each statement (A) and (R) regarding uniform motion.

### Step-by-Step Solution:

1. **Understanding Statement (A)**:
- The statement (A) claims that the velocity-time graph for an object in uniform motion along a straight path is a straight line parallel to the time axis.
- In uniform motion, the velocity of the object remains constant over time. This means that there is no change in velocity as time progresses.

2. **Drawing the Velocity-Time Graph**:
- On a graph, the x-axis represents time, and the y-axis represents velocity.
- Since the velocity is constant, the graph will be a horizontal line. This line is parallel to the time axis (x-axis).
- Therefore, statement (A) is **True**.

3. **Understanding Statement (R)**:
- The statement (R) claims that in uniform motion of an object, velocity increases as the square of the time elapsed.
- In uniform motion, the definition states that the velocity does not change; it remains constant. The relationship between velocity and time does not involve any increase or decrease.
- The equation for velocity in uniform motion is given by \( v = u + at \), where \( a \) (acceleration) is zero in uniform motion. Thus, \( v = u \), indicating that velocity remains constant and does not depend on time.

4. **Conclusion on Statement (R)**:
- Since the velocity does not increase with time but remains constant, statement (R) is **False**.

5. **Final Evaluation**:
- Statement (A) is True, and Statement (R) is False.
- Therefore, the answer to the question is that (A) is true and (R) is false.