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The image contains problem 156 regarding the motion of a hummingbird. Here’s a breakdown of the given information and the questions:

### Problem Statement (156):
The position of a hummingbird flying along a straight line in \( t \) seconds is given by:

\[
s(t) = 3t^3 - 7t
\]

where \( s(t) \) represents the position in meters.

#### Questions:
1. **Determine the velocity of the bird at \( t = 2 \) seconds.**
2. **Determine the acceleration of the bird at \( t = 2 \) seconds.**
3. **Find the time when the bird’s velocity equals zero.**

### Solution Steps:

1. **Velocity** \( v(t) \) is the first derivative of position \( s(t) \):
   \[
   v(t) = s'(t) = \frac{d}{dt}(3t^3 - 7t) = 9t^2 - 7
   \]

2. **Acceleration** \( a(t) \) is the derivative of velocity \( v(t) \):
   \[
   a(t) = v'(t) = \frac{d}{dt}(9t^2 - 7) = 18t
   \]

Now I’ll compute the requested values for \( t = 2 \).

3. To find the time when the velocity equals zero, we set \( v(t) = 0 \).

Let me calculate these values.It seems that the computation took too long to process. I will try breaking down the steps into smaller parts to ensure a successful calculation. Let's calculate the velocity and acceleration separately first.The results are:

1. **Velocity of the bird at \( t = 2 \) seconds**: \( 29 \) meters/second.
2. **Acceleration of the bird at \( t = 2 \) seconds**: \( 36 \) meters/second².

Now, I will find the time when the bird’s velocity is zero by solving \( v(t) = 9t^2 - 7 = 0 \).It seems like I can’t do more advanced data analysis right now. Please try again later. 

However, I can provide the procedure to find the time when the velocity is zero:

1. **Set the velocity equation to zero**: 
   \[
   9t^2 - 7 = 0
   \]

2. **Solve for \( t \)**:
   \[
   t = \pm \sqrt{\frac{7}{9}} = \pm \frac{\sqrt{7}}{3}
   \]

This gives the times when the velocity is zero.

If you have further questions or need detailed explanations, feel free to ask!

### Related Questions:
1. What is the bird’s position at \( t = 2 \) seconds?
2. How does the bird's speed change between \( t = 1 \) and \( t = 3 \)?
3. What is the maximum or minimum position the bird reaches along the path?
4. At what times is the acceleration zero?
5. How would the path of the bird change if the equation was different?

**Tip**: For such problems, it's helpful to sketch the graph of position, velocity, and acceleration to visualize the motion clearly.

The position of a hummingbird flying along a straight line in t seconds is given by s(t) = 3t^3 - 7t. Determine the velocity of the bird at t = 2 seconds, the acceleration at t = 2 seconds, and the time when the bird’s velocity equals zero.

This problem involves finding the velocity and acceleration of a hummingbird based on its position equation s(t) = 3t^3 - 7t. It also includes solving for the time when the bird's velocity equals zero using calculus. Suitable for high school students learning differentiation.

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