AI Tutor
If you sprint an entire 400-meter lap around a track, your legs burn and your watch logs 400 meters of effort. Yet in physics, your overall change in position is exactly zero.
How can you travel hundreds of meters and still end up with zero progress? To answer that, we must establish how physicists map motion in one dimension.

Position on a Line

Position (xx) is the exact location of an object at a specific moment relative to a chosen reference point called the origin (x=0x = 0).
Because motion along a straight line happens in two opposite directions, we assign signs: positive values lie to the right of the origin, and negative values lie to the left.
When an object moves from one position to another, how do we track the journey versus the final outcome?

Distance vs. Displacement

Distance (dd) is a scalar quantity representing the total length of the path traveled, meaning it depends only on magnitude and is always positive or zero (dβ‰₯0d \ge 0).
Displacement (Ξ”x\Delta x) is a vector quantity representing the straight-line change in position from initial position xix_i to final position xfx_f, defined as Ξ”x=xfβˆ’xi\Delta x = x_f - x_i.
Let's work through a multi-step problem to see how direction flips affect each calculation.

Worked Example: The Robot Delivery