D

Step 1: Analyze the displacement-time graph. The graph shows that the displacement is constant after the time \(t_0\), indicating that the particle is not moving at that time.
Step 2: Before \(t_0\), the graph shows a linear increase in displacement, implying that the particle is moving in the positive x direction with constant velocity.
Step 3: After \(t_0\), the displacement does not change, so the particle is at rest.
Therefore, the particle moves at a constant velocity up to time \(t_0\) and then stops.
Thus, the correct answer is D.