Unit 1 · Kinematics

Scalar ● (core concept) — A quantity described by magnitude only. Distance and speed are scalars.

Vector ● (core concept) — A quantity described by both magnitude and direction, drawn as an arrow whose length is proportional to its magnitude. Position, displacement, velocity, and acceleration are vectors.

Vector addition in one dimension ○ — In a one-dimensional coordinate system, opposite directions are given opposite signs and vectors add algebraically; the sign of a component fully describes its direction.

Vector notation ○ — Vectors are written with an arrow above the symbol (e.g., v with an arrow); in one dimension the sign of a component completely describes its direction.

Object model ○ — A modeling choice that ignores an object's size, shape, and internal structure, treating it as a single point with properties such as mass.

Displacement ● (core concept) — The change in an object's position: final position minus initial position (Δx = x − x₀). Displacement is a vector.

Average velocity ● (core concept) — Displacement divided by the time interval over which it occurs: v_avg = Δx/Δt.

Average acceleration ● (core concept) — Change in velocity divided by the time interval: a_avg = Δv/Δt. An object is accelerating whenever the magnitude or direction of its velocity changes.

Instantaneous velocity and acceleration ● (core concept) — The velocity or acceleration at a single instant, found by averaging over a very small time interval.

Kinematic equations (constant acceleration) ● (core concept) — For motion with constant acceleration: v_x = v_x0 + a_x·t; x = x_0 + v_x0·t + ½·a_x·t²; v_x² = v_x0² + 2·a_x·(x − x_0). They apply in any direction as appropriate.

Gravitational acceleration ● (core concept) — Near Earth's surface, gravity causes a constant downward acceleration of approximately 10 m/s², independent of the object's mass.

Motion graphs ● (core concept) — On a position–time graph, the instantaneous velocity is the slope of the tangent line; on a velocity–time graph, the instantaneous acceleration is the slope of the tangent line. Displacement is the area under a velocity–time graph, and change in velocity is the area under an acceleration–time graph.

Reference frame ● (core concept) — The coordinate system an observer uses to measure motion. The measured direction and magnitude of motion quantities depend on the chosen frame.

Relative velocity ● (core concept) — Motion measured in one frame can be converted to another by adding vectors: an object's velocity equals its velocity relative to an observer plus the observer's velocity relative to the frame.

Inertial reference frame ● (core concept) — A reference frame in which an observer would verify Newton's first law. The acceleration of an object is the same as measured from all inertial frames, and on the AP exam the frame may be assumed inertial unless stated otherwise.

Vector components ● (core concept) — A vector can be modeled as the resultant of two perpendicular components and resolved into components with a chosen coordinate system using sine, cosine, and tangent.

Projectile motion ● (core concept) — Two-dimensional motion with zero acceleration in one dimension and constant, nonzero acceleration in the other. It is analyzed by separating the motion into two independent one-dimensional motions.