Science:Math Exam Resources/Courses/MATH103/April 2009/Question 01 (e)
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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
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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).