1.2 Representations of Motion

Position, velocity, and acceleration

Position describes where an object is relative to a reference point. Velocity is the rate of change of position (includes direction), and acceleration is the rate of change of velocity. These quantities are related through derivatives: velocity is the slope of a position-time graph, and acceleration is the slope of a velocity-time graph.

Reading motion graphs

On a position-time graph, slope = velocity; a curved line means changing velocity (acceleration). On a velocity-time graph, slope = acceleration, and the area under the curve equals displacement. Motion diagrams show dots at equal time intervals — spacing that grows means speeding up, shrinking means slowing down.

Multiple representations of the same motion

The same motion can be shown using words, motion diagrams, data tables, graphs (x-t, v-t, a-t), and equations. Being able to translate between these representations is key: a constant slope on an x-t graph corresponds to a horizontal line on a v-t graph, and a flat line on a v-t graph means zero acceleration.

Key terms

Position

An object's location relative to a chosen reference point; represented by x.

Velocity

The rate of change of position with time; the slope of an x-t graph.

Acceleration

The rate of change of velocity with time; the slope of a v-t graph.

Area under a v-t graph

Represents the displacement of the object over that time interval.

Motion diagram

A series of images/dots showing an object's position at equal time intervals; spacing reveals speeding up, slowing down, or constant velocity.

Try an AP-style question

What does the slope of a position vs. time graph represent?

1. Velocity
2. Acceleration
3. Distance
4. Displacement