AP Physics 1 Unit 1 Notes: Two-Dimensional Kinematics (Algebra-Based)

Reference frame

A chosen viewpoint/coordinate system (plus an implied observer) used to measure position, time, and motion.

Observer (in a frame)

The entity assumed at rest in the chosen reference frame, used to define measured positions and velocities.

Inertial frame

A non-accelerating reference frame where Newton’s laws and constant-acceleration kinematics apply in their usual form.

Non-inertial frame

An accelerating reference frame in which motion descriptions become more complicated (often requiring extra/“fictitious” forces in advanced treatments).

Relative motion

The idea that measured motion depends on the reference frame; velocities and positions compare an object to a chosen frame or other object.

Relative velocity notation (v_{A/C})

The velocity of object A as measured in the reference frame of C (read “A relative to C”).

Relative velocity addition (vector form)

A rule for changing frames: 𝐯{A/C} = 𝐯{A/B} + 𝐯_{B/C}.

Relative displacement addition (vector form)

A frame-change rule for displacement over the same time interval: Δ𝐫{A/C} = Δ𝐫{A/B} + Δ𝐫_{B/C}.

Vector

A quantity with magnitude and direction (e.g., displacement, velocity, acceleration, force).

Scalar

A quantity with magnitude only (e.g., time, mass, temperature, speed).

Component form of a vector

Writing a vector as ordered components, e.g., 𝐯 = ⟨vx, vy⟩, to handle 2D motion algebraically.

Vector magnitude from components

For components (Ax, Ay), the magnitude is A = √(Ax² + Ay²).

Component relations (cos/sin)

For magnitude A at angle θ from +x: Ax = A cosθ and Ay = A sinθ.

Vector addition in components

If 𝐀 = ⟨Ax, Ay⟩ and 𝐁 = ⟨Bx, By⟩, then 𝐀+𝐁 = ⟨Ax+Bx, Ay+By⟩.

Vector subtraction in components

If 𝐀 = ⟨Ax, Ay⟩ and 𝐁 = ⟨Bx, By⟩, then 𝐀−𝐁 = ⟨Ax−Bx, Ay−By⟩.

Collinear vectors

Vectors that lie along the same line (same or opposite directions); only in this case do magnitudes add/subtract directly with signs.

Sign convention

A consistent choice of positive direction(s) so 1D relative motion can be handled with signed numbers.

Component method (2D relative motion)

Solving relative-motion problems by writing separate x- and y-component equations and adding components rather than magnitudes.

Projectile

An object moving under gravity alone (air resistance neglected), so acceleration is constant and downward.

Gravitational acceleration (g)

The magnitude of Earth’s downward acceleration near the surface, about 9.8 m/s² (often with a_y = −g if +y is up).

Separate-axes principle (2D kinematics)

In 2D constant-acceleration motion, apply 1D kinematics independently in x and y; the only shared variable linking them is time.

Horizontal acceleration in projectile motion (a_x)

For ideal projectile motion (no air resistance), ax = 0, so vx remains constant.

Vertical acceleration in projectile motion (a_y)

For ideal projectile motion with +y up, ay = −g, so vy changes linearly with time.

Time of flight (level-ground projectile)

Total time in the air; when launch and landing heights match, it can be found via vertical motion symmetry (time up = time down).

Range (projectile motion)

The horizontal displacement during flight; commonly found by Δx = v_{0x}·t using the flight time from vertical motion.