AP Physics C: Mechanics Unit 1 Cheatsheet: Kinematics

Representations:

• Arrow diagrams: length ∝ magnitude, arrow points in direction
• Unit vector notation: r⃗ = (Aî + Bĵ + Ck̂)
• Magnitude + direction angle

Vector Addition (Resultant):

C⃗ = A⃗ + B⃗ = (A_x + B_x)î + (A_y + B_y)ĵ

Sign Convention: Opposite directions in 1D use opposite signs (+ and −).

Displacement: Change in position

Δx = x − x₀

Average Velocity: Displacement per unit time

v⃗_avg = Δx⃗ / Δt

Average Acceleration: Change in velocity per unit time

a⃗_avg = Δv⃗ / Δt

Key Insight: Acceleration occurs when magnitude or direction of velocity changes (or both).

Small Time Intervals: As Δt → 0, average values approach instantaneous values.