Motion Graphs

Overview

This lesson turns motion into graph language. You need to be able to read what a graph says, decide which quantity is changing, and use gradients or areas to calculate the missing information.

What You Need to Know

• Distance and speed are scalars. Displacement, velocity, and acceleration are vectors, so direction matters.
• On a displacement-time graph, the gradient gives velocity.
• On a velocity-time graph, the gradient gives acceleration and the area under the graph gives displacement.
• A curved graph means the gradient is changing. Use a tangent if you need an instantaneous value.

How to Work Through It

1. Start by matching the five key motion quantities to their meanings and units.
2. Practise reading straight-line and curved displacement-time graphs.
3. Use velocity-time graphs to find acceleration from gradients and displacement from area.
4. Compare descriptions of motion with the graphs that represent them.

Check Your Understanding

• What does a negative gradient mean on a displacement-time graph?
• How can a velocity-time graph show motion in the opposite direction?
• Why does the area under a velocity-time graph give displacement, not distance?
• How would you estimate the gradient at one point on a curve?

Common Mistakes

• Confusing distance with displacement when direction changes.
• Treating every graph as if its gradient has the same meaning.
• Forgetting that area below the time axis is negative displacement.
• Reading a point value when the question asks for a gradient or area.

Next Steps

• Keep a short table of graph rules in your notes.
• Bring these graph ideas into the SUVAT lesson, where the same quantities appear in equation form.