In class, we had modeled Usain Bolt's record-breaking sprint as a constant acceleration phase followed by a constant velocity phase. One could also model his sprint as a velocity that increases to a constant value at the finish line. Because the velocity initially changes, the acceleration will initially be non-zero; however, the velocity is constant at the end, so the acceleration is zero there. This means the acceleration cannot be constant. The simplest function with a variable acceleration would be a cubic position function. Let's model his sprint with a cubic position function: x(t) = at + bt + ct +d %3D Let's assume he starts from rest at the origin of the x-axis at time t = 0. Usain Bolt's sprint was for the 100 m dash, which he completed with at time of 9.58 s. Think about how a sprinter would run a race and determine what is known about his initial and final position, velocity, and acceleration. Do not calculate any of these quantities; these are either known or unknown from the statement of the problem. If any of these value are not known (not given), then enter "?", otherwise, enter its value. Remember that we are assuming his velocity increases to a constant value at the end of the race. t(s) x(m) Vx(m/s) ay(m/s?) 9.58 Check
In class, we had modeled Usain Bolt's record-breaking sprint as a constant acceleration phase followed by a constant velocity phase. One could also model his sprint as a velocity that increases to a constant value at the finish line. Because the velocity initially changes, the acceleration will initially be non-zero; however, the velocity is constant at the end, so the acceleration is zero there. This means the acceleration cannot be constant. The simplest function with a variable acceleration would be a cubic position function. Let's model his sprint with a cubic position function: x(t) = at + bt + ct +d %3D Let's assume he starts from rest at the origin of the x-axis at time t = 0. Usain Bolt's sprint was for the 100 m dash, which he completed with at time of 9.58 s. Think about how a sprinter would run a race and determine what is known about his initial and final position, velocity, and acceleration. Do not calculate any of these quantities; these are either known or unknown from the statement of the problem. If any of these value are not known (not given), then enter "?", otherwise, enter its value. Remember that we are assuming his velocity increases to a constant value at the end of the race. t(s) x(m) Vx(m/s) ay(m/s?) 9.58 Check
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![### Modeling Usain Bolt's Sprint
In class, we had modeled Usain Bolt's record-breaking sprint as a constant acceleration phase followed by a constant velocity phase. One could also model his sprint as a velocity that increases to a constant value at the finish line. Because the velocity initially changes, the acceleration will initially be non-zero; however, the velocity is constant at the end, so the acceleration is zero there. This means the acceleration cannot be constant. The simplest function with a variable acceleration would be a cubic position function.
#### Let's model his sprint with a cubic position function:
\[ x(t) = at^3 + bt^2 + ct + d \]
Let's assume he starts from rest at the origin of the x-axis at time \( t = 0 \). Usain Bolt's sprint was for the 100 m dash, which he completed with a time of 9.58 s.
---
### Exercise
Think about how a sprinter would run a race and determine what is known about his initial and final position, velocity, and acceleration. **Do not calculate any of these quantities**; these are either known or unknown from the statement of the problem. If any of these values are not known (not given), then enter "?"; otherwise, enter its value. Remember that we are assuming his velocity increases to a constant value at the end of the race.
| t(s) | x(m) | v_x (m/s) | a_x (m/s²) |
|------|------|-----------|------------|
| 0 | | | |
| 9.58 | | | |
[Check Button]
---
#### Instructions
1. Identify the initial and final values for position, velocity, and acceleration at \( t = 0 \) and \( t = 9.58 \) seconds.
2. Fill out the table based on your understanding.
3. Click "Check" to submit your answers.
This exercise is intended to help you understand the fundamentals of kinematics using real-world examples. By modeling Usain Bolt's sprint, you can explore concepts like varying acceleration, initial and final conditions in motion, and cubic functions as a model for physical phenomena.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff5bd1a27-e559-4abd-b158-898799f60d66%2Fc11bf868-e311-4360-9a85-f75135c9cadb%2Fjl2rt87_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Modeling Usain Bolt's Sprint
In class, we had modeled Usain Bolt's record-breaking sprint as a constant acceleration phase followed by a constant velocity phase. One could also model his sprint as a velocity that increases to a constant value at the finish line. Because the velocity initially changes, the acceleration will initially be non-zero; however, the velocity is constant at the end, so the acceleration is zero there. This means the acceleration cannot be constant. The simplest function with a variable acceleration would be a cubic position function.
#### Let's model his sprint with a cubic position function:
\[ x(t) = at^3 + bt^2 + ct + d \]
Let's assume he starts from rest at the origin of the x-axis at time \( t = 0 \). Usain Bolt's sprint was for the 100 m dash, which he completed with a time of 9.58 s.
---
### Exercise
Think about how a sprinter would run a race and determine what is known about his initial and final position, velocity, and acceleration. **Do not calculate any of these quantities**; these are either known or unknown from the statement of the problem. If any of these values are not known (not given), then enter "?"; otherwise, enter its value. Remember that we are assuming his velocity increases to a constant value at the end of the race.
| t(s) | x(m) | v_x (m/s) | a_x (m/s²) |
|------|------|-----------|------------|
| 0 | | | |
| 9.58 | | | |
[Check Button]
---
#### Instructions
1. Identify the initial and final values for position, velocity, and acceleration at \( t = 0 \) and \( t = 9.58 \) seconds.
2. Fill out the table based on your understanding.
3. Click "Check" to submit your answers.
This exercise is intended to help you understand the fundamentals of kinematics using real-world examples. By modeling Usain Bolt's sprint, you can explore concepts like varying acceleration, initial and final conditions in motion, and cubic functions as a model for physical phenomena.
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