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In class, we had modeled Usain Bolt's record-breaking sprint as a constant acceleration phase followed by constant velocity phase. One could also model his sprint as a velocity that increases to a constant value at t 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 timet = 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) ax(m/s?) 9.58 100 10.44 1.09 Check

In class, we had modeled Usain Bolt's record-breaking sprint as a constant acceleration phase followed by constant velocity phase. One could also model his sprint as a velocity that increases to a constant value at t 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 timet = 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) ax(m/s?) 9.58 100 10.44 1.09 Check

College Algebra (MindTap Course List)
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter5: Exponential And Logarithmic Functions
Section5.2: Applications Of Exponential Functions
Problem 43E
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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 timet = 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) ax (m/s²) 9.58 100 10.44 1.09 Check
Transcribed Image Text: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 timet = 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) ax (m/s²) 9.58 100 10.44 1.09 Check
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