Speed, Calculations & Distance Time Graphs

Overview

This lesson moves the topic from measurement into description of motion. Keep the links between words, equations, and graphs visible at all times so you see that “at rest”, “constant speed”, and “accelerating” are the same ideas in several forms.

What You Need to Know

• Use the definitions of speed and velocity to decide whether direction matters in a question.
• Introduce scalar and vector language briefly so you can classify common motion quantities correctly.
• Model the speed and average-speed equations with direct substitution before mixing units or rearrangement.
• Keep distance-time and speed-time graphs side by side so you compare what slope and shape mean on each graph.
• Try one clear graph example to show that the gradient of a distance-time graph gives speed, and one clear area-under-graph example to show distance from a speed-time graph.

How to Work Through It

1. Start with a short measurement recap and a prediction question about what makes one object “faster” than another.
2. Work through speed, velocity, and average speed with quick calculation examples.
3. Move into graph interpretation, comparing distance-time and speed-time shapes and the motion they represent.
4. Finish with mixed questions that combine graph reading with one gradient or area calculation.

Check Your Understanding

• Check whether you can classify named quantities as scalar or vector with a reason.
• Try one hinge question where you choose which graph shows constant speed, rest, or acceleration.
• Give a straight-line distance-time graph and check whether you can calculate the speed from its gradient.

Common Mistakes

• Confusing speed-time and distance-time graphs. Keep the vertical axis meaning explicit every time a graph is shown.
• Some assume a line going down on any graph means slowing down. Use examples to show that graph type matters.
• Area under a speed-time graph is sometimes mistaken for acceleration. Contrast gradient and area on the same graph.

Next Steps

• Use the worksheet to practise mixed equation and graph questions.
• Carry forward the graph interpretation skills into the acceleration lesson.