Final answer:
The time intervals in which a particle moves in the positive and negative directions can be determined by analyzing the position-versus-time and velocity-versus-time graphs.
Step-by-step explanation:
The time intervals in which a particle moves in the positive direction and the negative direction can be determined by analyzing the position-versus-time and velocity-versus-time graphs. In the positive direction, the particle moves when the position-versus-time curve has a positive slope, indicating that the object is moving away from the origin. In the negative direction, the particle moves when the position-versus-time curve has a negative slope, indicating that the object is moving towards the origin.
For example, if we observe a positive slope on the position-versus-time curve between 0 and 0.5 seconds, we can infer that the particle is moving in the positive direction during that time interval. On the other hand, if we observe a negative slope on the position-versus-time curve between 1.0 and 2.0 seconds, we can infer that the particle is moving in the negative direction during that time interval.