- #1
wirefree
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Question:
I have a function of time. Its expression has a constant 'b' in it. I am asked to ascertain how changing 'b' affects the function.
Specifically, I have velocity as a function of time which accounts for drag forces; 'b' is the drag coefficient. I am asked to ascertain how changing 'b' affects how quickly terminal velocity is attained.
Attempt 1:
I understand that Calculus is the study of change. I am tempted to employ it. Hence, I obtained the derivative of the velocity function [tex] \frac{dv}{db}[/tex]
Trouble:
My limited understanding also tells me 'derivatives' help me determine how quickly a function changes given a change in one of its variables. I doubt if that's what my velocity-b context is demanding.
Attempt 2:
I have also labored through studying [tex]v(t)[/tex] graphs for different values of 'b'.
Trouble:
I am not in favor of the method from Attempt 2 since it's labor-intensive and, perhaps, crude (do you agree?).Any guidance as to how to address this question would be greatly appreciated.wirefree
I have a function of time. Its expression has a constant 'b' in it. I am asked to ascertain how changing 'b' affects the function.
Specifically, I have velocity as a function of time which accounts for drag forces; 'b' is the drag coefficient. I am asked to ascertain how changing 'b' affects how quickly terminal velocity is attained.
Attempt 1:
I understand that Calculus is the study of change. I am tempted to employ it. Hence, I obtained the derivative of the velocity function [tex] \frac{dv}{db}[/tex]
Trouble:
My limited understanding also tells me 'derivatives' help me determine how quickly a function changes given a change in one of its variables. I doubt if that's what my velocity-b context is demanding.
Attempt 2:
I have also labored through studying [tex]v(t)[/tex] graphs for different values of 'b'.
Trouble:
I am not in favor of the method from Attempt 2 since it's labor-intensive and, perhaps, crude (do you agree?).Any guidance as to how to address this question would be greatly appreciated.wirefree