Topic Cluster

Kinematics

Kinematics: position, velocity and acceleration — the mathematical language for describing how things move through space and time, before you ask what causes it.

Kinematics — the core equations of kinematics, and every article on the topic
The equations this topic keeps coming back to.

What Is Kinematics?

Kinematics is the branch of mechanics that describes motion — position, velocity and acceleration — without asking what causes it. Get these five equations straight and most of introductory physics stops being guesswork.

Core equations in kinematics
RelationshipEquationWhat it tells you
Average velocityv = Δs / ΔtDisplacement per unit time
Accelerationa = Δv / ΔtRate of change of velocity
First SUVATv = u + a·tFinal velocity from acceleration and time
Second SUVATs = u·t + ½·a·t²Displacement under constant acceleration
Third SUVATv² = u² + 2·a·sVelocity without needing the time
Projectile rangeR = v²·sin(2θ) / gHorizontal range of a projectile
Relative Velocity Explained
Kinematics

Relative Velocity Explained

Relative velocity is the velocity one body has as measured by another, and it is a subtraction of vectors rather than a comparison of speeds: v_AB = v_A - v_B, component by component, with both velocities written in one common frame. The consequence catches almost everyone out. Reversing one body leaves its speed untouched and changes the sign of what you subtract, so two cars at 100 and 80 km/h give 20 km/h the same way round and 180 km/h head-on. This page sets out the convention and the symbol table, the river crossing in both of its forms, the drift and crab angles of a crosswind, why relative speed is not closing speed, where a simple subtraction finally fails, and eight problems worked step by step.

26 min read
Jerk in Physics: What Happens When the Acceleration Itself Changes
Kinematics

Jerk in Physics: What Happens When the Acceleration Itself Changes

Jerk in physics is the rate at which an acceleration changes, and it is the quantity the familiar displacement formula has nowhere to put. Hold it constant and one more term appears, a sixth of the jerk times the time cubed, which is exactly what a constant-acceleration equation leaves out. Four of the five formulas a reader might reach for miss by exact amounts, including the one that looks most like a definition. Eight worked problems, three original diagrams, an interactive lab and a calculator.

21 min read