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can you please do (d) and (e)?
![**Problem 3:** An amusement park ride rotates around a fixed axis such that the angular position of a point on the ride follows the equation:
\[
\theta(t) = a + bt^2 - ct^3
\]
where \( a = 1.1 \) rad, \( b = 0.45 \) rad/s\(^2\) and \( c = 0.035 \) rad/s\(^3\).
**Randomized Variables**
- \( a = 1.1 \) rad
- \( b = 0.45 \) rad/s\(^2\)
- \( c = 0.035 \) rad/s\(^3\)
---
**Part (a)** Determine an equation for the angular speed of the ride as a function of time, \(\omega(t)\).
- **Expression**: \(\omega(t) =\) __________________________
Select from the variables below to write your expression. Note that all variables may not be required.
β, θ, a, b, c, d, g, h, j, k, m, n, P, S, t
---
**Part (b)** Besides at \( t = 0 \), at what time \( t_1 \) is the ride stopped? Give your answer in seconds.
- **Numeric**: A numeric value is expected and not an expression.
\[ t_1 = \] __________________________
---
**Part (c)** What is the magnitude of the angular displacement of the ride in radians between times \( t = 0 \) and \( t = t_1 \)?
- **Numeric**: A numeric value is expected and not an expression.
\[ \Delta \theta = \] __________________________
---
**Part (d)** Determine an equation for the angular acceleration of the ride as a function of time, \(\alpha(t)\).
- **Expression**: \(\alpha(t) =\) __________________________
Select from the variables below to write your expression. Note that all variables may not be required.
β, θ, a, b, c, d, g, h, j, k, m, n, P, S, t
---
**Part (e)** What is the angular acceleration in rad/s\(^2\) when the ride is at rest at \( t = t_1 \)?
- **Numeric**: A numeric value is expected and not](https://content.bartleby.com/qna-images/question/fa043fe4-4451-42e8-82d1-21cc59f9ce63/01cf42e1-0865-43a4-8cc7-1879f592f0ac/ak23b5_processed.jpeg)
Transcribed Image Text:**Problem 3:** An amusement park ride rotates around a fixed axis such that the angular position of a point on the ride follows the equation:
\[
\theta(t) = a + bt^2 - ct^3
\]
where \( a = 1.1 \) rad, \( b = 0.45 \) rad/s\(^2\) and \( c = 0.035 \) rad/s\(^3\).
**Randomized Variables**
- \( a = 1.1 \) rad
- \( b = 0.45 \) rad/s\(^2\)
- \( c = 0.035 \) rad/s\(^3\)
---
**Part (a)** Determine an equation for the angular speed of the ride as a function of time, \(\omega(t)\).
- **Expression**: \(\omega(t) =\) __________________________
Select from the variables below to write your expression. Note that all variables may not be required.
β, θ, a, b, c, d, g, h, j, k, m, n, P, S, t
---
**Part (b)** Besides at \( t = 0 \), at what time \( t_1 \) is the ride stopped? Give your answer in seconds.
- **Numeric**: A numeric value is expected and not an expression.
\[ t_1 = \] __________________________
---
**Part (c)** What is the magnitude of the angular displacement of the ride in radians between times \( t = 0 \) and \( t = t_1 \)?
- **Numeric**: A numeric value is expected and not an expression.
\[ \Delta \theta = \] __________________________
---
**Part (d)** Determine an equation for the angular acceleration of the ride as a function of time, \(\alpha(t)\).
- **Expression**: \(\alpha(t) =\) __________________________
Select from the variables below to write your expression. Note that all variables may not be required.
β, θ, a, b, c, d, g, h, j, k, m, n, P, S, t
---
**Part (e)** What is the angular acceleration in rad/s\(^2\) when the ride is at rest at \( t = t_1 \)?
- **Numeric**: A numeric value is expected and not
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