https://file.aiquickdraw.com/mathbot/file/1724607120344lvjwvphl.jpg

https://file.aiquickdraw.com/mathbot/file/1724607120346mbazbtfo.jpg

To work on part (d) of the problem, I will first extract the mathematical content from the image. Let's start by identifying and interpreting the relevant equation.

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### Problem Recap:
Given the equation \( s = t^3 - 6t^2 + 9t \):

### Part (d) asks:
- Determine the time when the acceleration of the object is zero.

### Steps to Solve:
1. **Find the velocity \( v(t) \)**: Velocity is the first derivative of position \( s(t) \) with respect to time \( t \).

2. **Find the acceleration \( a(t) \)**: Acceleration is the first derivative of velocity \( v(t) \) with respect to time \( t \), or the second derivative of \( s(t) \).

3. **Set \( a(t) = 0 \)**: Solve for \( t \) when acceleration is zero.

Let me compute this.The time when the acceleration of the object is zero is \( t = 2 \) seconds.

Would you like more details on any specific part, or do you have further questions?

Here are some related questions you might consider:

1. What is the velocity of the object at \( t = 2 \) seconds?
2. How would you find the position of the object at \( t = 2 \) seconds?
3. Can the object have multiple instances when acceleration is zero?
4. What does the velocity function tell us about the motion of the object?
5. How does the acceleration relate to the concavity of the position-time graph?

**Tip:** Understanding how to derive and solve differential equations is crucial for analyzing motion in physics and engineering.

Explore how to find the time when acceleration of an object is zero using calculus. Step-by-step solution for the equation s = t^3 - 6t^2 + 9t. Learn about velocity, acceleration, and their derivatives. Suitable for college-level physics and engineering students.

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