MATH103 April 2009
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Question 01 (e)
Multiple Choice question: Select ONE correct answer. You will not be graded for any work.
A charged molecule moves in a changing electric field which results in an acceleration of a(t) = cos(t) (in appropriate units). At time t = 0, the molecule is at rest at position x(0) = 1. What is the position x(t) when the molecule's velocity reaches the value -1 for the first time after time 0?
(e) The velocity never reaches -1
Make sure you understand the problem fully: What is the question asking you to do? Are there specific conditions or constraints that you should take note of? How will you know if your answer is correct from your work only? Can you rephrase the question in your own words in a way that makes sense to you?
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The acceleration is the second derivative of the position .
With we find, that we need to solve the differential equation
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We find, that we need to solve the differential equation
We integrate and get .
With we find .
We continue with integrating , which leads to .
With we find and get .
The velocity beeing reaches at , and we get
So, the answer is (d).
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