Topic 1.2: The Kinematic Equations

Name: _______________________________ Date: _______________

Before We Start: Yesterday's Recap

Yesterday we learned to add vectors using components. Without looking back: what are the two formulas for finding a vector's x- and y-components?

Today's New Concepts

AP CED Alignment: Unit 1, Topics 1.2/1.3

The Four Kinematic Equations (constant acceleration only)

$v = v_i + at$ (no Δx)
$\Delta x = v_it + \tfrac{1}{2}at^2$ (no v)
$v^2 = v_i^2 + 2a\Delta x$ (no t)
$\Delta x = \tfrac{1}{2}(v_i + v)t$ (no a)

The "5 Variables, 4 Equations" Trick

The five variables are vᵢ, v, a, Δx, and t. Every equation above uses 4 of the 5 and leaves exactly ONE out (noted next to each equation above). To pick the right equation: figure out which variable is missing from the problem (not asked for, and not given), then use the equation that also leaves that variable out.

Where Equation 2 Comes From — Galileo

Galileo discovered $\Delta x \propto t^2$ for an object starting from rest and undergoing constant acceleration. In modern notation, that's $\Delta x = \tfrac{1}{2}at^2$ (the vᵢ = 0 case of equation 2 above). Adding a nonzero starting velocity gives the full equation: $\Delta x = v_it + \tfrac{1}{2}at^2$.

Common Mistake

For constant acceleration starting from rest, the AVERAGE velocity is NOT the same as the final velocity — the final velocity is exactly double the average. (Example: starting from rest, ending at 40 m/s → average velocity over that time is 20 m/s, not 40.)

Keep This Sheet!

These sheets build into your semester study guide. Keep them in order in a binder or folder — you'll want to flip back through them before quizzes, unit tests, and when AP exam review starts in the spring.