Kinematics
Kinematics is the branch of mechanics that describes motion — position, velocity, and acceleration — without considering the forces that cause it. Its core tools are the kinematic equations relating displacement, velocity, acceleration, and time.
Kinematics is the study of how objects move: where they are, how fast they travel, and how their velocity changes over time. It deliberately ignores why motion occurs — forces and mass belong to dynamics — and focuses purely on describing motion with the quantities displacement, velocity, and acceleration. Each is a vector, so direction matters: velocity is the rate of change of position, and acceleration is the rate of change of velocity.
For motion with constant acceleration, a small set of kinematic equations connects these quantities. The most used are v = v₀ + at, Δx = v₀t + ½at², and v² = v₀² + 2aΔx, where v₀ is initial velocity, a is acceleration, and t is time. Free fall is the classic application: near Earth's surface, objects accelerate downward at about 9.8 m/s², so a dropped ball's speed after 2 seconds is roughly 19.6 m/s. Projectile motion extends the same equations to two dimensions by treating horizontal and vertical motion independently.
Kinematics also has a rotational counterpart. Angular position, angular velocity, and angular acceleration obey equations of identical form (for example, ω = ω₀ + αt), letting the same problem-solving approach describe spinning wheels and rotating machinery.
Kinematics is foundational on physics-based exams. The AP Physics 1 exam tests linear and rotational kinematics through graphs, equations, and conceptual questions, and the FE Civil exam covers kinematics within its dynamics topic, where particle motion problems reuse these same relationships.
Key takeaways
- Kinematics describes motion using displacement, velocity, and acceleration, without reference to forces.
- The constant-acceleration equations — v = v₀ + at, Δx = v₀t + ½at², v² = v₀² + 2aΔx — solve most problems.
- Free fall and projectile motion are standard applications, with vertical acceleration of about 9.8 m/s² near Earth's surface.
- Rotational kinematics mirrors linear kinematics with angular quantities.
- AP Physics 1 and the FE Civil exam both test kinematics through equation-based and graphical problems.