In Lesson 1-1-2, a flat line meant "stopped." On a velocity-time graph, a flat line means the exact opposite kind of stability — cruising at a constant speed. Same shape, different meaning, because the vertical axis changed.
slope = velocity
slope = acceleration
🧭 Plot Summary
You already know how to read a graph — Lesson 1-1-2 built that muscle. Today the vertical axis changes from position to velocity, and almost every rule you trusted gets a twist. The height of the line now tells you velocity directly — no slope math required. The slope becomes something new: acceleration, the rate at which velocity itself is changing.
There's one more move, and it's brand new: the area between the line and the time axis gives you displacement. A rectangle's area is base times height; a triangle's area is half of that. Break a v-t graph into simple shapes, and you can find how far an object went without a single motion detector in sight.
The core distinction
What you will do in this lesson
- Flip the rule from Lesson 1-1-2: on a v-t graph, height IS the velocity — no slope-reading required.
- Find acceleration from the slope of a v-t graph, and read it directly off the height of an a-t graph.
- Untangle 'speeding up' and 'slowing down' from the plain sign of velocity or acceleration alone.
- Use area under a v-t graph to recover displacement — a brand-new move for this unit.
- Build the three-graph hierarchy: x-t, v-t, and a-t all describe the same motion from different angles.
Why it matters
Lesson 1-2-2 hands you the kinematic equations, which are really just algebraic shortcuts for the area and slope relationships you'll build by hand today. If area-under-the-curve doesn't make sense yet, the equations in 1-2-2 will feel like memorized nonsense instead of something you can derive.
✅ Self-Check Before You Roll On
Check off each item as you get there. These are not grades — they are your own signal.