To solve this problem, we need to determine the rate of acceleration for the tilt of an amusement park ride. The central piece of information given is that the angular acceleration rate is [tex]\( 2160 \frac{\text{degrees}}{\text{min}^2} \)[/tex].
Here's how we can understand and interpret this information step by step:
1. Understanding Acceleration:
- Acceleration is the rate of change of velocity with respect to time.
- In this context, the velocity being referred to is angular velocity, which changes in degrees per minute ([tex]\(\frac{\text{degrees}}{\text{min}}\)[/tex]).
- The acceleration given is angular acceleration, which measures how quickly the tilt angle's velocity is changing, hence the unit [tex]\(\frac{\text{degrees}}{\text{min}^2}\)[/tex].
2. Given Data:
- The problem states that the ride's tilt has an angular acceleration of [tex]\(2160 \frac{\text{degrees}}{\text{min}^2}\)[/tex].
3. Interpreting the Solution:
- This angular acceleration means that every minute, the angular velocity of the ride's tilt is increasing by [tex]\(2160 \frac{\text{degrees}}{\text{min}}\)[/tex].
- No further calculations are needed because the problem is straightforwardly providing the rate of angular acceleration directly.
4. Conclusion:
- The ride's tilt is accelerating at [tex]\( 2160 \frac{\text{degrees}}{\text{min}^2}\)[/tex].
Thus, the detailed understanding of the question and interpretation of the data provided leads us to conclude that the rate of angular acceleration for the tilt of the amusement park ride is:
[tex]\[
2160 \frac{\text{degrees}}{\min^2}
\][/tex]
