Final answer:
The average acceleration of a particle moving at a constant speed in a circular path is equal to its centripetal acceleration. For a particle moving at π m/s in a circular path of radius 12 m, the centripetal (and thus the average) acceleration over 6 seconds remains constant and can be calculated using the formula ac = v²/r.
Step-by-step explanation:
A student inquired about the magnitude of average acceleration for a particle moving at a constant speed of π m/s around a circular track with a radius of 12 m over a time interval of 6 s. Centripetal acceleration is the relevant concept here since the particle is in circular motion. The formula for centripetal acceleration is ac = v²/r, where 'v' is the velocity and 'r' is the radius of the circular path.
Since the speed is constant, there is no tangential acceleration, which means that the total acceleration of the particle can be considered as just the centripetal acceleration. Plugging in the given values, the centripetal acceleration ac would be (π m/s)² / 12 m = π² / 12 m/s². The average acceleration over the time interval, because the speed does not change, would remain the same as the centripetal acceleration calculated.