Concept preview

What you will be able to do

1. 01Model straight-line motion with a position function $s(t)$, and compute velocity $v(t)=s'(t)$ and acceleration $a(t)=v'(t)=s''(t)$ as successive derivatives.
2. 02Use the SIGN of velocity to determine direction of motion and speed $|v(t)|$ to measure how fast, and identify when a particle is at rest ($v=0$).
3. 03Decide when a particle is speeding up or slowing down by comparing the signs of $v$ and $a$, and distinguish total distance travelled from displacement.

Picture a particle moving back and forth along a straight line, like a bead on a wire. Its POSITION is given by a function $s(t)$: a signed coordinate on the line at time $t$, where positive means one direction from the origin and negative means the other. Position is a location, not a distance — it can be negative, and the particle can return to a spot it has visited before. Everything we want to know about the motion is encoded in this one function and its derivatives.