Question why is there a negative sign

[camboguy]

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.

 

[Nabeshin]

I have no clue. They just randomly decided to flip the signs on everything, it looks like =/

 

[nlightner]

The negative sign in the solution for (b) represents the direction of motion of the particle. In the given equation, the coefficient of t^2 is negative, which means that the particle is moving in the negative direction along the c axis. This is because as t increases, the value of x decreases, indicating that the particle is moving in the opposite direction of the positive c axis.

When the particle returns to its initial position at t = 0, its velocity will also be in the opposite direction of its initial velocity, which is why the negative sign is included in the solution. This is a common convention in physics, where negative values represent motion in the opposite direction.

In summary, the negative sign in the solution represents the direction of motion of the particle and is necessary to accurately describe its velocity when it returns to its initial position.