Derivation of y = bt^2 for velocity and acceleration

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SUMMARY

The altitude of the space shuttle during its ascent is modeled by the equation y = bt², where b equals 2.9 m/s². The derivative for velocity, y', is calculated as y' = 2bt, while the second derivative for acceleration, y'', is y'' = 2b. The book incorrectly states the expressions for velocity and acceleration as y' = bt and y'' = b, leading to confusion. The correct expressions are essential for understanding the shuttle's motion during the first 30 seconds of ascent.

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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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