Final answer:
The position function describes the motion of a particle along a line. For x(t) = 4.0 - 2.0t m, the particle crosses the origin at t = 2.0 s and has a displacement of -6.0 m between t = 3.0 s and t = 6.0 s.
Step-by-step explanation:
The position function of a particle moving along a horizontal line is given by various equations depending on the scenario presented in the question. For a particle described by the position function x(t) = 4.0 - 2.0t m, we answer two parts:
- (a) To find when the particle crosses the origin, we set x(t) = 0, which gives us t = 2.0 s.
- (b) The displacement of the particle between t = 3.0 s and t = 6.0 s can be found by evaluating the position function at these times and finding their difference, resulting in -6.0 m.
For motion in one dimension, the acceleration, velocity, and position functions provide a complete description of a particle's motion. Position functions help to determine factors such as crossing points, displacement, and trajectory.