Final answer:
To determine the acceleration of particle A at point O, we need to analyze the velocity versus time graphs for particle A and particle B. The acceleration of particle A at point O is equal to the acceleration of particle B at that point. Without more specific information or a specific graph to refer to, we cannot determine the exact acceleration value.
Step-by-step explanation:
To determine the acceleration of particle A at point O, we need to analyze the velocity versus time.graphs for particle A and particle B. Since the velocity versus time graph for particle A is tangent to the velocity versus time graph for particle B at point O, the acceleration of particle A at point O is equal to the acceleration of particle B at that point.
Therefore, to find the acceleration of particle A at point O, we need to find the slope of the velocity versus time graph for particle B at point O. The slope of the graph represents the acceleration.
Without more specific information or a specific graph to refer to, it is not possible to determine the exact value of the acceleration at point O. Therefore, none of the given options (a) -0.85 meters/second², b) 1.16 meters/second², c) -1.16 meters/second², d) -0.9 meters/second²) can be definitively considered as the correct answer.