Final answer:
The overall displacement Δx of a particle is found by subtracting the initial position (xo) from the final position (xf), following the formula Δx = xf - xo.
Step-by-step explanation:
The overall displacement Δx of a particle is calculated by taking the final position xf and subtracting the initial position xo. This is denoted by the equation Δx = xf - xo. Displacement represents the change in position of the particle and has both magnitude and direction, making it a vector quantity.
In this context, if we want to calculate the displacement between t = 3.0 s and t = 6.0 s for a particle moving along the x-axis with the position function x(t) = 4.0 - 2.0t m, we would plug the times into the position function to determine xo and xf and then use our displacement equation to find Δx. The SI unit for displacement is the meter (m), but other units of length may be used and converted if necessary.