A massive space freighter wants to accelerate at 1g. 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 1g) is: "refer to the picture". The captain wants to reach 1g at time t = T. What must A be, to satisfy a(T) = 1g?
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1) A massive space freighter wants to accelerate at 1g. 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 1g) is: "refer to the picture". The captain wants to reach 1g at time t = T. What must A be, to satisfy a(T) = 1g?
2) The desired final acceleration is now 4g, with a corresponding value for A. Recall the equation in the picture. Acceleration feels like a 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 find T (in seconds) such that the maximum value of a'(t) is 1/80 m/s3.
3) Now, A = 0.6 and T = 2800 seconds. The freighter begins at rest and reaches the desired acceleration in time T. Now calculate and answer v(T) in m/s.
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