What is Kinematics?
The branch of mathematics (and physics) that describes the motion of objects, focusing on displacement, velocity, acceleration, and distance — without reference to the forces causing the motion.
In IB Math AA SL, kinematics problems are a direct application of differentiation and integration. The motion of a particle along a straight line is described using three interconnected quantities:
- Displacement — the position of the particle relative to a fixed origin (a vector quantity)
- Velocity — the rate of change of displacement (a vector quantity)
- Acceleration — the rate of change of velocity (a vector quantity)
In IB kinematics, motion is almost always along a straight line. The sign of and indicates direction — typically positive means right/forward, negative means left/backward.
The Fundamental Relationships
The three kinematic quantities are linked through calculus. These two relationships are the backbone of every kinematics problem:
Differentiation (going "forward"):
Integration (going "backward"):
You can think of it as a chain:
Every time you integrate, you introduce a constant of integration . Always use an initial condition — such as or — to find .