Answer :
Final answer:
Thus, the particle can have an acceleration of magnitude 20.00 m/s² with a combination of centripetal and tangential accelerations.
Explanation:
The question asks if a particle moving with an instantaneous speed of 8.00 m/s on a path with a radius of curvature of 4.00 m can have an acceleration of magnitude 20.00 m/s². To determine the validity of this statement, we need to consider the centripetal acceleration that is required for an object to move in a circle.
The formula to calculate centripetal acceleration ‘a’ is a = v²/r, where ‘v’ is the velocity and ‘r’ is the radius of curvature. Plugging in the given values, we calculate the centripetal acceleration as (8.00 m/s)² / 4.00 m = 16.0 m/s².
The calculated centripetal acceleration is less than the stipulated 20.00 m/s². However, this does not mean that the particle cannot have a total acceleration of 20.00 m/s². The total acceleration can still be 20.00 m/s² if there is an additional tangential acceleration component that is perpendicular to the centripetal acceleration.
Thus, the particle can have an acceleration of magnitude 20.00 m/s² with a combination of centripetal and tangential accelerations.
