The position of a particle moving along the x -axis is given...

The position of a particle moving along the $x$ -axis is given by $x(t)=4.0-2.0 t \mathrm{m} .$ (a) At what time does the particle cross the origin? (b) What is the displacement of the particle between $t=3.0 \mathrm{s}$ and $t=6.0 \mathrm{s} ?$

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Key Concepts

Position-Time Relationship

This concept describes how the position of a particle varies with time, often represented by a function x(t). Understanding this relationship allows one to determine the location of the particle at any given moment and forms the basis for analyzing motion along a line.

Constant Velocity Motion

When the position-time function is linear, it implies that the particle moves with a constant velocity. This means the particle covers equal distances in equal intervals of time, simplifying the analysis of its motion, including predicting its position and calculating displacement.

Solving Linear Equations

This is the process of finding the value of a variable that satisfies an equation. In the context of motion, setting the position function equal to a certain value (like zero for crossing the origin) and solving the resulting linear equation helps determine the specific time at which a particular event occurs.

Displacement

Displacement is defined as the change in position of an object between two points in time. It is calculated as the final position minus the initial position, and it provides a vector quantity that indicates both the magnitude and direction of the movement irrespective of the actual path taken.

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