Final answer:
The question pertains to high school level Physics, dealing with the motion of an object in a horizontal plane, where the object's position, velocity, and acceleration are analyzed over time.
Step-by-step explanation:
The question involves analyzing the motion of an object, considering its position, velocity, and acceleration as functions of time, specifically in the context of horizontal movement. This looks at the scenario of projectile motion without considering vertical motion, taking ax = 0, which means there is no horizontal acceleration. This is a typical high school physics problem that requires understanding of kinematics.
To find the time at which a particle crosses the origin given the function x(t) = 4.0 - 2.0t m, set x(t) = 0 and solve for t. For displacement calculation between t = 3.0 s and t = 6.0 s, substitute these times in the x(t) function and calculate the difference in positions to find displacement. The velocity as a function of time is obtained by differentiating the position function x(t).