Final answer:
The tire makes approximately 54 revolutions during the motion. The final rotational speed of the tire is approximately 3.50 revolutions per second.
Step-by-step explanation:
To find the number of revolutions the tire makes during the motion, we need to find the distance traveled by the tire. We can use the formula for average speed: speed = distance / time. Rearranging the formula, we can find the distance: distance = speed x time. Plugging in the given values, we get distance = 22 m/s x 9 sec = 198 m.
Since the distance traveled by the tire is equal to the circumference of the tire, we can calculate the number of revolutions using the formula: number of revolutions = distance / circumference. The circumference of the tire is 2 x π x radius = 2 x π x 0.58 m = 3.64 m. Plugging in the values, we get number of revolutions = 198 m / 3.64 m = 54.40, which can be rounded to 54 revolutions.
To find the final rotational speed of the tire in revolutions per second, we divide the final angular speed by the time taken. The final angular speed can be found using the formula: final angular speed = initial angular speed + angular acceleration x time. Since the car started from rest, the initial angular speed is 0. We can use the equation for uniform acceleration: angular acceleration = change in angular speed / time. Plugging in the values, we get angular acceleration = (22 rad/s - 0 rad/s) / 9 s = 2.44 rad/s². Plugging in the values, we get final angular speed = 0 rad/s + 2.44 rad/s² x 9 s = 21.96 rad/s.
Finally, to find the final rotational speed in revolutions per second, we divide the final angular speed by 2π (since there are 2π radians in one revolution). Plugging in the value, we get final rotational speed = 21.96 rad/s / (2 x π) ≈ 3.50 revolutions per second.