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AP Course

AP Physics C: Mechanics

Updated for the AP Physics C: Mechanics framework effective fall 2024, with calculus-based derivations, labs, quizzes, and practice.

Build calculus-based mechanics with original derivations, experiments, quizzes, and practice sets.

Lessons
Scalars and VectorsDisplacement, Velocity, and AccelerationRepresenting MotionReference Frames and Relative MotionMotion in Two or Three DimensionsSystems and Center of MassForces and Free-Body DiagramsNewton’s Third LawNewton’s First LawNewton’s Second LawGravitational ForceKinetic and Static FrictionSpring ForcesResistive ForcesCircular MotionTranslational Kinetic EnergyWorkPotential EnergyConservation of EnergyPowerLinear MomentumChange in Momentum and ImpulseConservation of Linear MomentumElastic and Inelastic CollisionsRotational KinematicsConnecting Linear and Rotational MotionTorqueRotational InertiaRotational Equilibrium and Newton’s First Law in Rotational FormNewton’s Second Law in Rotational FormRotational Kinetic EnergyTorque and WorkAngular Momentum and Angular ImpulseConservation of Angular MomentumRollingMotion of Orbiting SatellitesDefining Simple Harmonic Motion (SHM)Frequency and Period of SHMRepresenting and Analyzing SHMEnergy of Simple Harmonic OscillatorsSimple and Physical Pendulums
Quizzes
Practice Problems Formula notes, diagrams, and practice sets will be added here.

AP Physics C: Mechanics · Unit 1 · Topic 1.3

Representing Motion

Calculus connects motion graphs and functions through derivatives, integrals, vectors, and reference frames.

1. Topic Lens

Representing Motion is studied through kinematics. Connect the system boundary, interacting parts, and measurable evidence before applying a formula.

\[v=\frac{dx}{dt},\quad a=\frac{dv}{dt}\]

2. Why the Formula Works

The relationship is built from definitions and conservation reasoning:

  1. Instantaneous velocity is defined as the derivative of position.
  2. Invert the derivative locally: dx=v(t)dt.
  3. Integrate over the interval and apply the initial position as the integration constant.
\[x(t)=x_0+\int_{t_0}^{t}v(t')\,dt'\]

3. Detailed Visual Model

Pixel diagram for Representing MotionOriginal schematic connecting Representing Motion to Kinematics.
Representing Motion: an original pixel-style model. Use it as a schematic, not a literal scale drawing.

4. Worked Example and Lab Link

Given v(t)=3t² m/s and x(0)=1 m, find x(2 s).

Answer: x=1+∫₀²3t²dt=1+8=9 m.

Investigation idea: Fit a smooth function to motion-sensor data, then compare numerical derivatives and integrals with measured quantities.

Common trap: An integration constant carries physical initial conditions; never drop it without justification.

Checkpoint · Topic 1.3

Explain how representing motion supports or limits this conclusion: x=1+∫₀²3t²dt=1+8=9 m.

Official curriculum reference: College Board AP Physics C: Mechanics course page. The explanation and worked example are independently written for this study site.