AI Tutor
If you sprint an entire 400Β m400\text{ m} lap around an Olympic track at record speed, your net displacement at the finish line is exactly zero meters. How can you be completely exhausted if physics says you ended up nowhere?
Position (ss or xx) describes where an object sits relative to a chosen reference point called the origin (OO). While distance is a scalar measuring the total path length traveled, displacement (Ξ”s\Delta s) is a vector measuring straight-line change in position: Ξ”s=sfinalβˆ’sinitial\Delta s = s_{\text{final}} - s_{\text{initial}}.
Because displacement accounts for direction while distance does not, how do we describe how fast that position changes over time?

Velocity vs. Speed

Average speed is total distance divided by time elapsed, whereas average velocity (vˉ\bar{v}) is displacement divided by time: vˉ=ΔsΔt\bar{v} = \frac{\Delta s}{\Delta t}.
When you look at a car's speedometer, you see instantaneous speed, which is the magnitude of instantaneous velocity (v=lim⁑Δtβ†’0Ξ”sΞ”t=dsdtv = \lim_{\Delta t \to 0} \frac{\Delta s}{\Delta t} = \frac{ds}{dt}), representing the exact rate of change of position at a single moment.
What happens when your velocity is not constant, but changing from moment to moment?

Acceleration and Direction

Acceleration (aa) is the rate of change of velocity with respect to time (a=dvdt=d2sdt2a = \frac{dv}{dt} = \frac{d^2s}{dt^2}), measured in meters per second squared (mΒ sβˆ’2\text{m s}^{-2} or m/s2\text{m/s}^2).
A common trap is assuming negative acceleration always means 'slowing down'. An object speeds up whenever velocity and acceleration have the same sign, and slows down (decelerates) only when they have opposite signs.