how to do last part thanks
Hey hey! For a change in direction you are looking for the velocity being zero. To turn back, an object must first
stop completely (if we restrict to one-dimensional travel). So, looking at the previous parts of the question, simply solve for the x-values that cause your expression for velocity squared to be equal to zero!! You probably got the expression in this way.
Using initial conditions, we can find the constant and yield:
Now we can solve for this equal to zero (usual methods for solving a quadratic), and we obtain two solutions:
The answer we are looking for is x=1. Think of it this way, the particle starts moving towards the origin from the right. When it reaches x=1, it will turn around and go back the other way. From this point, it will never come back; we can gleam this from equations we have obtained. Acceleration is always positive, it is never going to be accelerated in the negative direction, it is going, going gone
Let me know if this doesn't make sense! It is kind of intuitive, which is a little easier than the rigorous mathematical approach (unnecessary for this question)