Position of toy moving on straight track

[dvdqnoc]

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.

 

[learningphysics]

The procedure you described should give you the answer... where did you get stuck?

 

[ogb p]

I would like to clarify that the given position equation for the toy locomotive is not complete without the inclusion of the initial position. The complete equation should be x = x0 + t^6 - 6t^2 + 9t, where x0 is the initial position of the toy locomotive. Without this information, it is not possible to accurately determine the position of the toy locomotive at any given time.

However, assuming that the initial position is zero, the net force on the locomotive can be calculated by taking the second derivative of the position equation, which gives us the acceleration equation a = 30t^4 - 12t + 9. Setting this equation to zero and solving for t, we get t = 0.3 seconds.

It is important to note that this solution assumes that there are no external forces acting on the toy locomotive and that it is moving in a straight line without any external disturbances. In a real-world scenario, this may not be the case and the net force on the locomotive may not be equal to zero at any given time. In such cases, a more detailed analysis would be required to accurately determine the position of the toy locomotive.