Question 3: What is the net force on a toy locomotive at t=3s?

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The position of a toy locomotive is described by the equation x = t^3 - 6t^2 + 9t. The net force on the locomotive is determined to be zero at t = 2 seconds, as derived from the second derivative of the position function. The user is learning LaTeX for mathematical typesetting and shared images of their work for feedback. Forum members emphasize that while they are willing to help with specific questions, they are not responsible for checking entire homework assignments. Overall, the discussion focuses on understanding the net force calculation for the locomotive.
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can someone check my work please thanks, oh btw I am still trying to learn how to use LaTeX mathematical typesetting; I figured itll be slightly faster taking a picture of the problem and my work and posting it here so please bare with me :redface:

1. The position of a toy locamotive moving on a straight track along the x-axis is given by the equation x = t^3 - 6t^2 + 9t, where x is in meters and t is in seconds. The net force on the locomotive is equal to 0 when t is equal to (a) zero (b) 2s (c) 3s (d) 4s (e) 5s


(my work)
x = t^3 - 6t^2 + 9t
v = 3t^2 - 12t -- first derivative
a = 6t - 12 -- second derivative
0 = 6t - 12
12 = 6t
t = 2s

Question 2: http://ourworld.cs.com/LezardV4leth/problem_2.jpg
Work: http://ourworld.cs.com/LezardV4leth/problem_2_work.jpg

Question 3: http://ourworld.cs.com/LezardV4leth/problem_3.jpg
Work: http://ourworld.cs.com/LezardV4leth/problem_3_work.jpg
 
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Looks ok to me...

BTW, don't count too much on us to systematically check your homework :smile:
We want to help with specific difficulties, misunderstandings or so, but we're not here to do the algebra checks for you :wink:
 
oh haha ^^;; Ill make note of that next time thanks a lot though
 

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