Use this as a quick reference for the kinematic equations, free fall, and the slope/area relationships between position, velocity, and acceleration graphs.
🧭 Plot Summary
The same motion can be told four ways — as a diagram, a graph, an equation, or a story — and this lesson is about moving fluently between all of them. For constant acceleration, three kinematic equations (vx = v0x + axt, x = x₀ + v0xt + ½axt², and vx² = v0x² + 2ax(x − x₀)) connect position, velocity, acceleration, and time — and near Earth's surface, that constant acceleration is almost always gravity, a = g ≈ 10 m/s², directed downward. Then there are the graphs: an x-t graph's slope gives velocity, a v-t graph's slope gives acceleration, and running that backward, the area under a v-t graph gives displacement while the area under an a-t graph gives the change in velocity.
What you'll do in this lesson
- Translate the same motion between motion diagrams, graphs, equations, and narrative descriptions.
- Apply the three constant-acceleration kinematic equations to find missing quantities.
- Use a = g ≈ 10 m/s², directed downward, for free-fall problems near Earth's surface.
- Read instantaneous velocity and acceleration as the slopes of tangent lines on x-t and v-t graphs.
- Read displacement and change in velocity as areas under v-t and a-t graphs.
Why it matters
This is where Unit 1's calculus becomes computable. The slope and area relationships you learn here — and the habit of reading a graph just as fluently as an equation — show up constantly for the rest of the course, especially once forces start producing more complicated accelerations in Unit 2.
✅ Self-Check Before You Roll On
Check off each item as you get there. These aren't grades — they're your own signal.