Every quantity in physics falls into one of two categories. A scalar is described by a single number — its magnitude. A vector is described by a magnitude and a direction. That one difference changes everything about how you work with these quantities.
Think about giving someone directions. "Walk 3 blocks" is a scalar instruction — just a distance. "Walk 3 blocks north" is a vector instruction — distance plus direction. For many physics problems, the direction is the whole point.
Physicists represent vectors as arrows. Two things about the arrow carry information:
Proportional to the magnitude. A longer arrow means a bigger vector.
The arrowhead points the way the vector acts. That's the direction.
A car moves at 20 m/s east, then brakes to 8 m/s east. Draw both velocity vectors and explain what changed.
The CED gives you a specific list. You need to know these cold — and more importantly, understand why each one is classified the way it is.
| Quantity | Type | Why | Symbol |
|---|---|---|---|
| Distance | Scalar | Just a total length — no direction. Always positive. | d |
| Speed | Scalar | How fast, with no regard to which way. Always positive. | v |
| Position | Vector | Where something is relative to an origin — direction matters. | x |
| Displacement | Vector | Change in position — has to know which way the change went. | Δx |
| Velocity | Vector | Speed with a direction. Can be positive or negative. | v |
| Acceleration | Vector | Change in velocity — direction tells you if it speeds up, slows down, or turns. | a |
In two or three dimensions you need actual vector notation to track direction. But in one dimension there are only two possible directions — and a positive or negative sign handles both of them perfectly.
You define which direction is positive at the start of a problem. Right and up are the usual defaults, but you can choose either direction — as long as you stay consistent throughout.
A ball is thrown upward at +15 m/s. It slows, stops, and falls back down. At what point is its velocity negative, and what does that mean?
When you add vectors in one dimension, you're doing signed arithmetic — the signs encode the directions, so adding vectors is just adding numbers with their signs included.
Use the tool below to build your intuition. Try making two vectors that cancel completely. Try making them both positive. Notice how the result changes.
Drag the sliders to set two vectors in 1D. Watch how the signs determine the result.
A person walks +8 m east, then −3 m west (back toward the origin). What is their total displacement? What total distance did they travel?
The CED introduces two forms of the same equation here — one using full vector notation for any dimension, and one simplified for one-dimensional motion.
Read this equation in plain English: final velocity equals starting velocity plus how much the velocity changed (acceleration × time). It's the definition of average acceleration rearranged into a more useful form.
A car starts from rest and accelerates at +4 m/s² for 6 seconds. What is its final velocity?