Which of the following statements are TRUE? Choose all that apply. [HINT: The statements that are false should contradict themselves or a definition.]

1. An object can simultaneously be moving and have zero velocity.

2. An object can simultaneously have zero velocity and have constant position.

3. An object can simultaneously have positive velocity and have constant acceleration.

4. An object can simultaneously have positive displacement and be traveling a positive distance.

5. An object can simultaneously be traveling a negative distance and have constant positive acceleration.

6. An object can simultaneously have positive acceleration and have positive velocity.

To determine which of the statements are true, we need to carefully analyze each statement. Let's go through them one by one:

1. An object can simultaneously be moving and have zero velocity.
To answer this statement, we need to recall the definition of velocity. Velocity is the rate at which an object changes its position with respect to time. If an object has zero velocity, it means that it is not changing its position. However, the statement mentions that the object is moving, which implies a change in position. Therefore, this statement contradicts itself. It is FALSE.

2. An object can simultaneously have zero velocity and have constant position.
Similar to the first statement, we need to consider the definition of velocity and position. Velocity measures the change in position over time. If an object has zero velocity, it means there is no change in position. Therefore, if an object has constant position, it implies that there is no change in its position over time. Therefore, this statement is TRUE.

3. An object can simultaneously have positive velocity and have constant acceleration.
Velocity and acceleration are related concepts. Velocity is the rate of change of position, while acceleration is the rate of change of velocity. Therefore, if an object has constant acceleration, it means its velocity is changing at a constant rate. Thus, the object cannot have a positive velocity at the same time, as that would mean its velocity is not changing. This statement contradicts itself and is therefore FALSE.

4. An object can simultaneously have positive displacement and be traveling a positive distance.
Displacement and distance are both measures of how far an object has moved. Displacement refers to the change in position, usually measured from a reference point. Distance, on the other hand, refers to the total path length traveled. Since the statement mentions positive displacement, it means the object has moved in a particular direction. If it is also traveling a positive distance, it means that the object is continuing to move in the same direction. Therefore, this statement is TRUE.

5. An object can simultaneously be traveling a negative distance and have constant positive acceleration.
Distance is a scalar quantity, representing the total length traveled regardless of direction. If an object is traveling a negative distance, it implies that the direction of travel has reversed. On the other hand, positive acceleration means that the object's velocity is increasing. Therefore, if an object is traveling a negative distance, its direction has changed, and it cannot have constant positive acceleration. This statement contradicts itself and is FALSE.

6. An object can simultaneously have positive acceleration and have positive velocity.
This statement is TRUE. In fact, positive acceleration often leads to positive velocity. Positive acceleration means that the object is speeding up, while positive velocity means that the object is moving in a positive direction. These two concepts are compatible with each other and can occur simultaneously.

In summary, the statements that are true are: 2 and 4.