Physics C: Mechanics · 10-15% of total exam weight · 14 min read · Updated 2026-05-11
Kinematics in One Dimension — AP Physics C: Mechanics
AP Physics C: Mechanics · 10-15% of total exam weight · 14 min read
1. Core Definitions of 1D Kinematics★☆☆☆☆⏱ 3 min
Kinematics is the branch of mechanics that describes the motion of objects without reference to the forces that cause motion. One-dimensional kinematics restricts all motion to a single straight line, so all motion quantities have only a magnitude and a sign (positive/negative, indicating direction along the line).
2. Calculus Relationships for Motion Quantities★★☆☆☆⏱ 4 min
All kinematic quantities are defined by relationships between position, time, velocity, and acceleration. Average quantities are defined over a finite time interval $\Delta t = t_f - t_i$:
To reverse this relationship (get velocity from acceleration, position from velocity), use integration with the constant of integration fixed by initial conditions:
When acceleration is constant ($a(t) = a$ for all $t$), the general integration rules simplify to a set of three widely used kinematic equations. These are extremely useful for problems like free fall, constant braking, etc., but are only valid when acceleration is constant.
\begin{aligned} v(t) &= v_0 + at \\ x(t) &= x_0 + v_0 t + \frac{1}{2} a t^2 \\ v^2 &= v_0^2 + 2a(x - x_0) \end{aligned}
4. Graphical Analysis of One-Dimensional Motion★★★☆☆⏱ 3 min
AP Physics C heavily tests the ability to interpret the three common motion graphs, with relationships that follow directly from calculus definitions:
On an $x$ vs $t$ graph: Slope at any point = instantaneous velocity; average slope between two points = average velocity.
On a $v$ vs $t$ graph: Slope at any point = instantaneous acceleration; net area under the graph between two times = displacement $\Delta x$.
On an $a$ vs $t$ graph: Area under the graph between two times = change in velocity $\Delta v$.
5. Additional Practice Worked Examples★★★☆☆⏱ 4 min
Common Pitfalls
Why: Students default to memorized simple equations even when acceleration is given as a function of time or position.
Why: Students confuse displacement (net change in position) with distance (total path length).
Why: Students forget the constant of integration is fixed by initial conditions, not zero by default.
Why: Students confuse the order of differentiation between position, velocity, and acceleration.
Why: Students memorize gravity as 9.8 m/s² and forget to adjust the sign to match the coordinate system.