AP Physics C: Mechanics - Core Concepts

Front

Scalar vs. Vector Quantities

Back

Scalars have magnitude only (distance, speed, mass, time, energy). Vectors have both magnitude and direction (displacement, velocity, acceleration, force, momentum). In kinematics, position, displacement, velocity, and acceleration are vectors. Vectors can be expressed in unit vector notation (i, j, k) or as magnitude with direction angle.

Front

Average Velocity and Average Acceleration

Back

Average velocity: v_avg = Δx/Δt (displacement divided by time interval). Average acceleration: a_avg = Δv/Δt (change in velocity divided by time interval). An object accelerates if either the magnitude OR direction of its velocity changes. Both are vector quantities.

Front

Kinematic Equations (Constant Acceleration)

Back

Four key equations: (1) v = v₀ + at, (2) x = x₀ + v₀t + ½at², (3) v² = v₀² + 2aΔx, (4) x = x₀ + ½(v + v₀)t. Use calculus to derive: v = dx/dt, a = dv/dt. Near Earth's surface, a_y = -g ≈ -10 m/s² (downward constant).

Front

Projectile Motion Analysis

Back

Projectile motion has zero horizontal acceleration (a_x = 0) and constant vertical acceleration (a_y = -g). Horizontal: x = x₀ + v₀ₓt. Vertical: y = y₀ + v₀ᵧt - ½gt². Treat x and y components independently. Time of flight determined by vertical motion; range determined by horizontal velocity and flight time.

Front

Relative Motion and Reference Frames

Back

Relative velocity is found by vector subtraction. For example, the velocity of A relative to B is \(\vec v_{A/B} = \vec v_A - \vec v_B\). Acceleration is the same in all inertial reference frames, and an inertial reference frame is one in which Newton’s first law holds.