Topic 1.3: Velocity-Time Graphs and Matching Graphs
Name: _______________________________ Date: _______________
Before We Start: Yesterday's Recap
Yesterday we learned acceleration. Without looking back: what's the formula for acceleration, and what does a negative value mean?
Today's New Concepts
AP CED Alignment: Unit 1, Topic 1.3
Velocity-Time Graph
- Plots velocity (vertical axis) against time (horizontal axis)
- Slope = acceleration. Steeper slope → greater acceleration. Flat line → constant velocity (zero acceleration).
- Area under the line = displacement. Works for rectangles (constant velocity) and triangles (constant acceleration from rest) alike.
Worked Example: A car speeds up steadily from 0 to 20 m/s over 5 s. $\text{Slope} = \dfrac{20-0}{5} = 4\text{ m/s}^2$ (acceleration). The graph forms a triangle with base 5 s, height 20 m/s → $\text{area} = \tfrac{1}{2}(5)(20) = 50\text{ m}$ (displacement).
The Three Graph Types, Side by Side
| Graph Type | What the SLOPE tells you | What the AREA tells you |
|---|---|---|
| Position-time (x-t) | Velocity | (not typically used) |
| Velocity-time (v-t) | Acceleration | Displacement |
| Acceleration-time (a-t) | (not typically used) | Change in velocity |
How to Move Between Graphs
- x-t → v-t: take the slope at each point. v-t → a-t: take the slope at each point.
- a-t → v-t: take the area under the curve. v-t → x-t (displacement): take the area under the curve.
Worked Example: An object starts at rest and undergoes constant positive acceleration. Its a-t graph is a flat line above zero. Its v-t graph is a straight line sloping upward from zero. Its x-t graph is a curve that gets steeper over time — NOT a straight line, because velocity itself keeps increasing.
Keep This Sheet!
This one is worth revisiting often — matching between these three graph types shows up constantly on the AP exam. Keep it at the front of your binder section for Unit 1.