Final answer:
On a position vs. time graph, the times when the speed of a particle is 0 m/s correspond to horizontal lines, indicating a constant position over a period of time, which means no movement and therefore zero velocity.
Step-by-step explanation:
To determine what time the speed of a particle is equal to 0 m/s while looking at a position vs. time graph, you must look for any portion of the graph where the position of the particle does not change over time. This would be indicated by a horizontal line on the graph.
Velocity is the slope of the position vs. time graph. Therefore, if there is a flat, horizontal section in this graph, it indicates that there is no change in position over time and the slope is zero - this means the velocity is 0 m/s. If a particle's velocity is zero and remains constant, it signifies that the particle is not moving for that period.
For instance, if a position vs. time graph shows a horizontal line from 0 to 2 seconds, it provés that during those 2 seconds the particle is stationary. Hence, the speed of the particle is 0 m/s starting from time zero and lasting until 2 seconds.