Kinematics — AP Physics 1
1. Foundations of Kinematics ★☆☆☆☆ ⏱ 2 min
Kinematics is the branch of classical mechanics that describes the motion of objects without considering the forces that cause motion. It is the foundational framework for all mechanics topics in AP Physics 1, making up 10-16% of your total exam score.
2. 1D Core Quantities: Scalars vs Vectors ★☆☆☆☆ ⏱ 3 min
One-dimensional (1D) motion describes motion along a straight line, and uses three core vector quantities (which have both magnitude and direction):
- **Position ($x$ / $y$):** Location relative to a defined origin. Displacement ($\Delta x$) is change in position: $\Delta x = x_{\text{final}} - x_{\text{initial}}$, distinct from distance (total path length, a scalar).
- **Velocity ($v$):** Rate of change of displacement. Average velocity: $v_{\text{avg}} = \frac{\Delta x}{\Delta t}$. Speed is the scalar magnitude of velocity, with no direction.
- **Acceleration ($a$):** Rate of change of velocity. Positive acceleration does not always mean speeding up: if velocity is negative, positive acceleration means slowing down.
Exam tip: Examiners frequently test the difference between scalars and vectors here, so always confirm if a question asks for a signed value (vector) or magnitude only (scalar).
3. Kinematic Equations for Constant Acceleration ★★☆☆☆ ⏱ 4 min
The four core kinematic equations below only apply when acceleration is constant, which is the case for nearly all AP Physics 1 kinematics problems. Each equation omits one variable, so you can choose the one that matches your known values to avoid extra calculations.
- $v = v_0 + at$ (no displacement term)
- $\Delta x = \frac{(v_0 + v)}{2}t$ (no acceleration term)
- $\Delta x = v_0 t + \frac{1}{2}at^2$ (no final velocity term)
- $v^2 = v_0^2 + 2a\Delta x$ (no time term)
Exam tip: Always select the equation that avoids calculating unnecessary intermediate variables to reduce arithmetic error and save exam time.
4. Free Fall and 2D Projectile Motion ★★☆☆☆ ⏱ 5 min
Free fall describes motion where the only acceleration is gravity (air resistance is always ignored in AP Physics 1 unless explicitly stated). The acceleration due to gravity $g = 9.8\ \text{m/s}^2$; if upward is defined as positive, free fall acceleration is always $a = -g$.
Projectile motion is 2D motion where only gravity acts, and horizontal and vertical motion are completely independent. Always split all quantities into horizontal ($x$) and vertical ($y$) components immediately:
- Horizontal axis: No acceleration, so horizontal velocity is constant: $\Delta x = v_{0x}t$, $v_{0x} = v_0\cos\theta$ where $\theta$ is launch angle.
- Vertical axis: Identical to 1D free fall: $v_{0y} = v_0\sin\theta$, $a_y = -g$.
5. Velocity-Time Graph Interpretation ★★☆☆☆ ⏱ 3 min
Velocity-time (v-t) graphs plot velocity on the y-axis and time on the x-axis, and two core rules are tested on nearly every AP Physics 1 exam:
- The **slope of the v-t graph equals acceleration**: a horizontal line means zero acceleration (constant velocity).
- The **net area under the v-t graph between two times equals net displacement**: area above the time axis is positive, area below is negative. Sum of absolute areas equals total distance traveled.
6. Reference Frames and Relative Velocity ★★★☆☆ ⏱ 3 min
All motion is measured relative to an inertial reference frame (a non-accelerating coordinate system where Newton's first law holds). There is no absolute rest frame, so velocity values depend on the frame they are measured in.
For relative velocity, if $v_A$ is velocity of A relative to ground, and $v_B$ is velocity of B relative to ground, the velocity of A relative to B is:
v_{AB} = v_A - v_B
For 2D relative velocity, calculate x and y components separately before combining.
Common Pitfalls
Why: Students incorrectly use distance/displacement and speed/velocity interchangeably.
Why: Students memorize the equations but forget their restricted use case.
Why: Students associate $g$ with a positive value and ignore direction conventions.
Why: Students use total initial velocity for both axes instead of splitting into components.
Why: Students memorize 'area = displacement' but forget sign conventions.