Final answer:
The displacement of a boulder from its initial position is zero when it returns to its starting point, regardless of the path taken. This can occur at multiple points in time, specifically when the boulder's position as a function of time equals its initial position.
Step-by-step explanation:
When considering the question of when the displacement of a boulder from its initial position is zero, it is important to understand the concept of displacement in the context of physics. Displacement is a vector quantity that refers to the change in position of an object. It is possible for a boulder to have a displacement of zero when it returns to its initial position, which means the initial and final positions are the same, regardless of the path the boulder may have taken.
For example, if a boulder rolls up a hill and then back down to its starting point, the displacement would be zero because it ends at the same point it started. If we apply this to the motion described by a position function, let's say x(t), displacement would be zero at any point in time where x(t)=x(0), the initial position. This can occur at t=0 or at any other time where the position function equals its initial value.
In a classic physics problem, if the boulder's velocity becomes zero at a certain time, and it subsequently returns to the starting point, the displacement at that time would also be zero. Using the given equations and understanding of physics, we can determine the precise moment(s) when the boulder's displacement is zero.