Motion Diagrams

A motion diagram shows snapshots of an object's position at equal time intervals. Each dot represents where the object is at a specific moment in time.

Reading Motion Diagrams

• Evenly spaced dots → constant velocity
• Dots getting farther apart → speeding up (accelerating)
• Dots getting closer together → slowing down (decelerating)
• Direction of dots → direction of motion

Watch how the object moves and leaves "ghost" positions behind at equal time intervals. Select different motion types to see how the pattern changes.

Motion diagrams are the most intuitive representation: you can literally see the motion as it happens over time.

Position-Time Graphs

Motion diagrams show position snapshots. position-time graph plots those same positions continuously, with time on the horizontal axis and position on the vertical axis.

Below is the same motion data from the diagram above, but now plotted as a position-time graph. Notice how the dots from the motion diagram become points on the curve.

Reading Position-Time Graphs

• Slope = velocity (steeper slope = faster speed)
• Straight line → constant velocity
• Curved line → changing velocity
• Positive slope → moving in positive direction
• Negative slope → moving in negative direction
• Horizontal line → not moving (velocity = 0)

Remember instantaneous velocity from the last section? It's the slope of the position-time curve at a specific point: the tangent line at that moment.

Velocity-Time Graphs

We just saw velocity as the slope of position-time graphs. Now let's plot velocity itself over time.

Below is the same motion data from above, but now showing velocity vs. time. Notice how different motion types create different patterns on the velocity-time graph.

Reading Velocity-Time Graphs

• Slope = acceleration (we'll get to this next)
• Area under curve = displacement
• Horizontal line → constant velocity (zero slope = no acceleration)
• Straight line (not horizontal) → constant acceleration
• Positive values → moving in positive direction
• Negative values → moving in negative direction

The area under a velocity-time graph gives you displacement. Think about it: velocity × time = displacement. On the graph, that's base × height = area of a rectangle (for constant velocity) or area under the curve (for changing velocity).

Acceleration

Position-time graphs show velocity through slope. Velocity-time graphs work the same way—their slope shows acceleration.

Defining Acceleration

Acceleration is the rate of change of velocity. It measures how quickly velocity is changing over time.

Like velocity, acceleration is a vector: the sign matters. But here's where it gets tricky.

The Sign of Acceleration

Positive acceleration doesn't always mean speeding up, and negative acceleration doesn't always mean slowing down. It depends on both the sign of velocity and acceleration:

• Positive velocity + positive acceleration → speeding up (moving forward faster)
• Positive velocity + negative acceleration → slowing down (moving forward slower)
• Negative velocity + negative acceleration → speeding up (moving backward faster)
• Negative velocity + positive acceleration → slowing down (moving backward slower)

Calculus Connection

In calculus, acceleration is the derivative of velocity with respect to time, just as velocity is the derivative of position. You don't need calculus to understand the concept: it's all about rates of change. But if you know calculus, you can see the pattern: position → velocity → acceleration, each step taking the derivative.