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May 23, 2015

Homework Help: Calculus (Related Rates)

Posted by Anonymous on Thursday, March 29, 2012 at 6:20pm.

The position of a particle moving in a straight line is given by s(t) = (e^(-t))(cos(5t)) for t>0, where t is in seconds. If the particle changes direction at time T seconds, then T must satisfy the equation:
cos(5T) = 0
5T = arctan(-1/5)
5e^(-t) sin(5t) = 0
tan(5T) = -1/5
cos(5T) = 5

I know that a change in direction will be marked by a change from positive to negative or vice versa, but I don't understand the equations the question gives me. Could someone please talk me through this process to find the right answer?

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