Final answer:
When the speed of a barrel rider moving in a circle is doubled, the new centripetal acceleration is calculated by squaring the ratio of the new speed to the old speed and multiplying by the original acceleration, resulting in an acceleration of 26.0 m/s².
Step-by-step explanation:
To find the new acceleration after the speed of the barrel rider is doubled, we need to understand that centripetal acceleration is directly proportional to the square of the speed and inversely proportional to the radius of the circular path. Given that the original speed is 7.5 m/s with an acceleration of 6.5 m/s², when the speed is doubled to 15.0 m/s, the new acceleration can be calculated using the ratio of the speeds squared.
Since the speed doubles, and the radius remains the same, the acceleration will increase by a factor of the square of the increase in speed. Thus, the new acceleration is 6.5 m/s² multiplied by (15.0 / 7.5)², which equals 6.5 m/s² × 4 = 26.0 m/s². Therefore, the correct answer is c. 26.0 m/s².