Kinematics
Describe where an object is, how its position changes, and how its velocity changes. The graphs and equations below are different views of the same motion.
How can one moving object produce three different graphs?
Start with position. Velocity tells how quickly position changes. Acceleration tells how quickly velocity changes. Nothing new is being invented at each step; we are reading the same history at a different level of change.
Each arrow means “rate of change with respect to time.”
Scrub one motion through time.
Velocity stays constant, so the position graph is a straight line. Equal time intervals add equal displacements.
Position
A coordinate gives location relative to a chosen origin and positive direction.
Displacement
Displacement compares final and initial position. It can be positive, negative, or zero.
Velocity
Velocity includes direction. Its sign tells which way position changes along the chosen axis.
Acceleration
Acceleration describes changing velocity. Negative acceleration does not automatically mean slowing down.
Three equations, one model.
When acceleration is constant, these equations are linked descriptions of the same motion. Choose the one whose known quantities match the question rather than treating them as unrelated formulas.
tracks position as time passes
tracks velocity as time passes
connects velocity directly to displacement
Constant acceleration makes position quadratic.
The squared time term is why the position graph bends into a parabola whenever acceleration is nonzero. The vertex can represent a physical turning point.
Open Patterns & Parabolas