Final answer:
In the context of relative motion, an object can be described as being both in motion and at rest when observed from different frames of reference. The example with two cars moving in opposite directions at the same speed illustrates this concept, as each driver sees the other as stationary relative to their own motion.
Step-by-step explanation:
In the given examples, the situation where both you and your friend could be correct in describing an object in motion and at rest respectively, is when dealing with frames of reference. Specifically, consider the scenario where you are driving a car at a constant velocity to the east (uniform motion) and your friend passes you in the opposite direction with the same speed. In your frame of reference, you perceive yourself as moving. However, in your friend's frame of reference, you appear to be stationary due to the relative motion where you and your friend are moving at the same speed in opposite directions.
This demonstrates a key concept in physics called relative motion, which is crucial in understanding that motion is not absolute but depends on the observer's frame of reference. Thus, both observations can be correct depending on the chosen frame of reference. This is different from the other options provided as they do not allow for both parties to observe the motion and rest simultaneously from their respective frames. Uniform circular motion, acceleration, or simple harmonic motion would not fit the criteria since these involve changes in direction or speed that are apparent in any frame of reference.