Unit Overview

Kinematics Overview

AP Physics C: Mechanics· 5 min read 📊 10-15% of total AP exam score

1. Unit at a Glance

Kinematics is the study of how objects move, and it builds the vocabulary you will use for every other unit in mechanics, from forces to energy to rotation. We start with motion along a single straight line to master core definitions and calculus relationships, then extend these same concepts to motion in two dimensions, including projectile motion, the most common 2D problem tested on the AP exam.

This unit is split into two connected sub-topics:

AP Physics C: Mechanics Kinematics in one dimension

Master core definitions, kinematic equations, and calculus relationships for motion along a straight line.

★★⏱ 15 min

AP Physics C: Mechanics Kinematics in two dimensions

Extend 1D kinematics rules to projectile motion and 2D vectors with independent motion components.

★★★⏱ 20 min

2. Common Pitfalls

Wrong move:

Mixing up the sign of acceleration for objects that are slowing down or moving downward.

Why:

Sign depends on your chosen coordinate system, not the direction of motion.

Correct move:

Define your coordinate system first, then assign signs to all quantities based on that system.

Wrong move:

Treating horizontal and vertical acceleration as linked in projectile motion.

Why:

The only acceleration in ideal projectile motion is vertical gravity; horizontal acceleration is always zero.

Correct move:

Solve horizontal and vertical motion problems independently, connecting them only through time.

3. Quick Reference Cheatsheet

Concept / Formula	Key Description
$v = \frac{d x}{d t}$ , $a = \frac{d v}{d t}$	Velocity as derivative of position; acceleration as derivative of velocity
$Δ x = \int_{t_{1}}^{t_{2}} v (t) d t$ , $Δ v = \int_{t_{1}}^{t_{2}} a (t) d t$	Displacement and velocity change from integration of motion quantities
$v = v_{0} + a t$ , $x = x_{0} + v_{0} t + \frac{1}{2} a t^{2}$ , $v^{2} = v_{0}^{2} + 2 a Δ x$	Kinematic equations for motion with constant acceleration
$a_{x} = 0$ , $a_{y} = - g$	Acceleration components for standard projectile motion (up = positive y)
$r (t) = x (t) \hat{i} + y (t) \hat{j}$	Vector representation of position in two-dimensional motion

What's Next

Start with the first sub-topic to build your foundational understanding of 1D kinematics, which is required for all subsequent material in this unit and the entire AP Physics C course. Mastering 1D concepts first makes extending to 2D kinematics much more intuitive. Once you complete both sub-topics here, you will move on to Newton's Laws of Motion, the next core unit of the course.