Velocity–time graphs

👩 Teacher’s Guide

🎯 Objective

Students will be able to:

Interpret velocity–time graphs for different motions
Use gradient to find acceleration from a v–t graph
Use area under the graph to find displacement

📝 Teaching Notes

Key idea to emphasize: Slope gives acceleration; area gives displacement.
Common misconception: Confusing area with acceleration or slope with speed.
Suggested teaching approach:
- Start with simple constant velocity line.
- Use rectangles/triangles for area calculations.
- Check signs for displacement direction.

💬 Discussion Starter

Ask students:

How can two journeys have the same average speed but different motion?
Why do units matter as much as the numbers?
How can graphs tell a story about motion?

🧒 Student Worksheet

Concept and Helping Material

A velocity–time graph shows how velocity changes. The gradient gives acceleration, and the area under the graph gives displacement (change in position).

Vocabulary and Definitions

— A graph of velocity (y) against time (x).
— The region under a graph; used to find displacement.
— Slope; gives acceleration on a v–t graph.
— Change in position; area under v–t graph with sign.
— Straight line with constant slope on v–t graph.

Hands-On Experiment or Activities

Activity 1: Area as Displacement
What You Need: graph sheets, ruler.
What You Do: Find displacement for a constant velocity section by area (rectangle).
Think and Talk: What changed? What stayed the same?

Activity 2: Triangles Under the Curve
What You Need: printed v–t graphs.
What You Do: Calculate displacement for accelerating motion using triangle + rectangle areas.
Think and Talk: What changed? What stayed the same?

Practice Questions (QA)

What does the gradient of a velocity–time graph represent?
What does the area under a velocity–time graph represent?
What does a horizontal line above zero mean?
What does a line sloping upward mean?
What does a line sloping downward to zero mean?
How do you calculate acceleration from the graph?
How do you find displacement for constant velocity?
If the graph crosses below zero, what does that mean?
What is the displacement if v = 3 m/s for 4 s?
Why include units on axes?

Reflection

Where do you see this idea in sports, travel, or everyday movement?
What is one measurement or graph habit that would improve your answers?