Question why is there a negative sign

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The discussion centers on the motion of a particle defined by the equation x = 2 + 3t - 4t², where x is in meters and t is in seconds. The confusion arises regarding the negative sign in the equation -x = -2 - 3t + 4t², which is used to determine the particle's velocity when it returns to its initial position at t = 0. The negative sign is necessary to express the position in terms of its return to the original state, ensuring that the equation reflects the change in direction of the particle. Understanding this concept is crucial for solving motion problems involving quadratic equations.

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A particle moves along the c axis. its position is given by the equation x = 2+3t-4t^2, with x in meters and t in seconds. Determine (a) its position when it changes direction and )b) its velocity when it returns to the position it had at t = 0.


i understand how to get (a) but for (b) I am confused why in the solution they put -x = -2-3t+4t^2 why is the negative there, i understand there is a change in direction at 0, I am confused why the negative sign is there can you give me a clear and understanding reasoning. thank you.
 
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I have no clue. They just randomly decided to flip the signs on everything, it looks like =/
 

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