This and the next two questions apply to this situation: A massive space freighter wants to accelerate at 4g. It takes time for the rocket engines to rev up, and turn up to their desired power. The freighter starts from rest, and its acceleration (until it reaches 4g) is: 3. 2t a(t) = -Ag 2t The captain wants to reach 4g at time t = T. What must A be, to satisfy a(T) = 4g?

College Physics
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ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
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Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
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This and the next two questions apply to this situation:
A massive space freighter wants to accelerate at 4g. It takes time for the rocket engines to rev up,
and turn up to their desired power. The freighter starts from rest, and its acceleration (until it
reaches 4g) is:
3
2t
a(t) = - Ag
2t
3
The captain wants to reach 4g at time t = T. What must A be, to satisfy a(T) = 4g?
Transcribed Image Text:This and the next two questions apply to this situation: A massive space freighter wants to accelerate at 4g. It takes time for the rocket engines to rev up, and turn up to their desired power. The freighter starts from rest, and its acceleration (until it reaches 4g) is: 3 2t a(t) = - Ag 2t 3 The captain wants to reach 4g at time t = T. What must A be, to satisfy a(T) = 4g?
The desired final acceleration is now 3g, with a corresponding value for A. Recall:
3
2t
2t
3
T
a(t)
-Ag
%3D
Acceleration feels like weight, and a rapid change in acceleration feels like a rapid change in weight.
You don't want a too rapid change in weight -- the derivative a'(t) shouldn't be too great. Therefore:
Take the derivative of a(t).
Find t that maximizes a'(t).
Answer T (in seconds) such that the maximum value of a'(t) is 1/60 m/s³.
(If this were the actual test, I would give you t. Here, I urge you to figure it out.)
Transcribed Image Text:The desired final acceleration is now 3g, with a corresponding value for A. Recall: 3 2t 2t 3 T a(t) -Ag %3D Acceleration feels like weight, and a rapid change in acceleration feels like a rapid change in weight. You don't want a too rapid change in weight -- the derivative a'(t) shouldn't be too great. Therefore: Take the derivative of a(t). Find t that maximizes a'(t). Answer T (in seconds) such that the maximum value of a'(t) is 1/60 m/s³. (If this were the actual test, I would give you t. Here, I urge you to figure it out.)
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