Derivation of y = bt^2 for velocity and acceleration

AI Thread Summary
The altitude of the space shuttle during its ascent is modeled by the equation y = bt^2, with b equal to 2.9 m/s². Calculating the first derivative, the velocity is expressed as y' = 2bt, while the second derivative, representing acceleration, is y'' = 2b. There is confusion regarding the book's answers, which state y' = bt and y'' = b. The discussion clarifies that the original calculations are correct, emphasizing the importance of distinguishing between velocity and acceleration. The thread highlights a discrepancy between the user's calculations and the textbook's responses.
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Homework Statement



The altitude of the space shuttle during the first 30 s of its ascent is described by the expression у = bt2, where the constant b has the value 2.9 m/s2. Using calculus, obtain an expression for the velocity and acceleration of the space shuttle during this period.


The Attempt at a Solution



y' = 2bt
y'' = 2b

Book is giving me the following for answers:
y' = bt
y'' = b

Am I doing something wrong?
 
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No, your answers are OK, as long as you are sure which is velocity and which is acceleration. I have no idea what the book was thinking by giving those answers.
 
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