Position of toy moving on straight track

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The position of a toy locomotive on a straight track is described by the equation x = t^6 - 6t^2 + 9t. To find when the net force on the locomotive is zero, the acceleration must be calculated by taking the second derivative of the position equation. The user attempted this method but expressed uncertainty about the correctness of their approach. Clarification is sought on the steps to accurately determine the time when the net force equals zero. The discussion emphasizes the importance of correctly applying calculus to solve the problem.
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Homework Statement


The position of a toy locomotive moving on a
straight track along the x-ais is given by the
equation

x = t^6 - 6t^2 + 9t

where x is in meters and t is in seconds.

The net force on the locomotive is equal to
zero when t is equal to _______?

Answer in units of s.


Homework Equations


x = t^6 - 6t^2 + 9t
http://www.glenbrook.k12.il.us/gbssci/phys/Class/1DKin/U1L6a1.gif

The Attempt at a Solution


I tried to get the acceleration equation by taking the second derivative of the position equation, setting it to zero, and solving for t... but doesn't look right.
 
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The procedure you described should give you the answer... where did you get stuck?
 

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