Motion Graphs - Complete Interactive Lesson
Part 1: Position-Time Graphs
๐ Position-Time Graphs
Part 1 of 7 โ Motion Graphs
Graphs are one of the most powerful tools in physics. A single position-time graph can tell you everything about an object's motion โ where it is, how fast it's going, and which direction it's moving โ all at a glance.
Reading Position-Time (-) Graphs
On a position-time graph:
- The horizontal axis is time ()
- The vertical axis is position ()
What the Graph Tells You
| Feature | Meaning |
|---|---|
| Point on the curve | Position at that time |
| Slope | Velocity |
| Positive slope | Moving in + direction |
| Negative slope | Moving in โ direction |
| Zero slope (flat) | Object is at rest |
| Straight line | Constant velocity |
| Curved line | Changing velocity (acceleration) |
The Key Relationship
The steeper the line, the faster the object moves.
Constant Velocity on - Graphs
When an object moves at constant velocity, the - graph is a straight line.
Examples
- Steep positive slope: fast motion in + direction
- Gentle positive slope: slow motion in + direction
- Negative slope: motion in โ direction
- Horizontal line: object at rest ()
Curved Lines: Non-Constant Velocity
When the - graph is curved, the velocity is changing โ the object is accelerating.
Reading Acceleration from Curvature
| Curve Shape | Motion |
|---|---|
| Curving upward (concave up) | Velocity is increasing (accelerating in + direction) |
| Curving downward (concave down) | Velocity is decreasing (decelerating) |
Instantaneous Velocity
For a curved graph, the instantaneous velocity at any moment is the slope of the tangent line at that point.
Average velocity = slope of the secant line (line connecting two points) Instantaneous velocity = slope of the tangent line (at a single point)
Concept Check โ Position-Time Graphs ๐ฏ
Reading Graphs โ Calculations ๐งฎ
A position-time graph shows a straight line passing through the points m and s m.
Graph Interpretation ๐
Exit Quiz โ Position-Time Graphs โ
Part 2: Velocity-Time Graphs
๐ Velocity-Time Graphs
Part 2 of 7 โ Motion Graphs
Velocity-time (-) graphs are arguably the most information-rich graphs in kinematics. From a single - graph, you can determine velocity, acceleration, AND displacement.
Slope = Acceleration
On a - graph:
Part 3: Acceleration-Time Graphs
๐ Acceleration-Time Graphs
Part 3 of 7 โ Motion Graphs
The third type of motion graph completes the picture. Acceleration-time (-) graphs show how acceleration varies over time. Just like with - graphs, the area under the curve carries physical meaning.
Reading - Graphs
Part 4: Slopes & Areas Under Curves
๐ Converting Between Graph Types
Part 4 of 7 โ Motion Graphs
One of the most important skills in AP Physics is translating between -, -, and - graphs. Each graph type contains enough information to construct the others (given initial conditions).
Part 5: Translating Between Graphs
๐ Non-Uniform Motion on Graphs
Part 5 of 7 โ Motion Graphs
So far we've focused mostly on constant velocity and constant acceleration. Now let's tackle more complex scenarios: objects that speed up, slow down, stop, and reverse โ all visible on their graphs.
Recognizing Direction Changes
On - Graphs
A direction reversal appears as a turning point (local max or min):
- The slope changes sign
- At the turning point, the slope is zero (momentary rest)
- Before: positive slope โ after: negative slope (or vice versa)
On - Graphs
Part 6: Problem-Solving Workshop
๐ ๏ธ Problem-Solving Workshop
Part 6 of 7 โ Motion Graphs
Time to sharpen your graph skills with a variety of practice problems. These problems mirror the style and difficulty of AP exam questions involving motion graphs.
Graph Reading Warm-Up ๐ฏ
Graph Conversion Practice ๐งฎ
An - graph shows:
- m/sยฒ from to s
Part 7: Synthesis & AP Review
๐ Synthesis & AP Review
Part 7 of 7 โ Motion Graphs
Let's consolidate everything about motion graphs. This review covers all three graph types, their relationships, and AP-level interpretation skills.
Complete Graph Relationships
The Derivative/Integral Chain
| Operation | From โ To | What It Gives |
|---|---|---|
| Slope | - โ - |