AP Physics C: Mechanics ›  Unit 0  ·  Supplementary

Unit 0 Calculus Primer

Not a College Board topic — just the calculus you'll actually use this year. Limits, derivative shortcuts, the chain rule, and integrals, taught with physics in mind from the very first example.

📋 Not AP Exam Content🕐 ~7–10 Class Periods📺 6 Episodes🧭 Self-Paced Review
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Episode Guide — Season 0

EP.0.1

Limits and Instantaneous Rate of Change

Average velocity is a slope between two points. Shrink the gap between those points to nothing, and you get the limit that makes “velocity at an instant” actually mean something.

lim(Δt→0) Δx/ΔtAverage vs. instantaneousWhy dx/dt makes sense
🕐 1–2 class daysOpen lesson →
EP.0.2

The Power Rule for Derivatives

You don't need limits every time — the power rule is the shortcut. This one rule is behind v = dx/dt, a = dv/dt, and most of the derivatives you'll ever take in this course.

d/dx(xⁿ) = nxⁿ⁻¹v = dx/dta = dv/dt
🕐 1–2 class daysOpen lesson →
EP.0.3

The Chain Rule

Functions inside functions need one more step: differentiate the outside, then multiply by the derivative of the inside. It shows up the moment position depends on something like sin(ωt + φ).

d/dt f(g(t)) = f'(g(t))·g'(t)Composite functionsDifferentiating sin(ωt + φ)
🕐 1–2 class daysOpen lesson →
EP.0.4

The Power Rule for Integrals

Integration undoes differentiation. The reverse power rule turns an acceleration function back into velocity, and velocity back into position.

∫xⁿ dx = xⁿ⁺¹/(n+1) + CAntiderivativesReversing the power rule
🕐 1–2 class daysOpen lesson →
EP.0.5

Definite Integrals and Area Under a Curve

A definite integral is just the area under a graph between two points. That's what makes Δx = ∫v dt, W = ∫F dx, and J = ∫F dt all make visual sense, not just algebraic sense.

∫ₐᵇ f(x)dx = F(b) − F(a)Area under a curveΔx = ∫v dt
🕐 1–2 class daysOpen lesson →
EP.0.6

Separable Differential Equations (Bonus)

Some equations mix a variable and its own derivative in the same breath. Separating them — variables on one side, everything else on the other — is the trick behind terminal velocity and the SHM solution you'll recognize later.

Separate the variables∫dv/(a − bv) = ∫dtUsed in 2.9 and 7.3
🕐 1–2 class daysOpen lesson →
🧭 No Progress Check for This Unit
Unit 0 isn't part of the AP Classroom sequence. Work through as much or as little as you need before Unit 1 starts.