Position velocity and acceleration

Describing where something is

Motion begins with position. Position tells where an object is compared with a chosen reference point. If you say a car is 20 meters east of a stop sign, the stop sign is the reference point and 20 meters east is the position. In physics, choosing a reference point matters because motion is always described relative to something.

Displacement is the change in position. If you walk from the front door of a house to a mailbox 12 meters away, your displacement might be 12 meters outward. If you walk to the mailbox and then back to the door, your total distance traveled is 24 meters, but your displacement is zero because you end where you started.

Speed and velocity

Speed tells how fast distance is covered. If a runner travels 100 meters in 10 seconds, the average speed is $10 m/s$. The basic relationship is $speed = distance/time$.

Velocity is similar to speed, but it includes direction. A car moving $20 m/s$ north and a car moving $20 m/s$ south have the same speed but different velocities. This difference matters because motion in physics often depends on direction. Velocity is a vector quantity, meaning it has both size and direction.

Average velocity compares displacement to time:

v_{avg} = rac{Delta x}{Delta t}

Here $Delta x$ means change in position, and $Delta t$ means change in time. The symbol $Delta$ means change in.

Acceleration

Acceleration describes how velocity changes. An object accelerates if it speeds up, slows down, or changes direction. This surprises many students because everyday speech often uses acceleration to mean only speeding up. In physics, turning a corner at constant speed is acceleration because the direction of velocity changes.

Average acceleration is:

a_{avg} = rac{Delta v}{Delta t}

The unit of acceleration is $m/s^2$, read as meters per second squared. This means the velocity changes by some number of meters per second each second. For example, an acceleration of $2 m/s^2$ means the velocity changes by $2 m/s$ every second.

Motion graphs

Graphs help us visualize motion. A position-time graph shows where an object is at different times. A steep line means the position changes quickly, so the object has a greater speed. A horizontal line means position is not changing, so the object is at rest.

A velocity-time graph shows how velocity changes. If the line is above zero, the object is moving in the positive direction. If the line slopes upward, velocity is increasing. If it slopes downward, velocity is decreasing or becoming more negative.

Constant velocity and constant acceleration

An object moving with constant velocity covers equal displacements in equal times. Its speed and direction do not change. An object moving with constant acceleration changes velocity by equal amounts in equal times. A falling object near Earth, ignoring air resistance, is a common example of nearly constant acceleration.

These ideas are the foundation of kinematics, the study of motion without yet asking what causes the motion. Forces come later. First we need a clear language for describing motion itself.

The big idea

Position tells where something is. Velocity tells how position changes. Acceleration tells how velocity changes. These three ideas allow us to describe motion clearly before explaining it with forces. Once you understand them conceptually, the equations become less like memorized rules and more like concise descriptions of change.