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Distance measures total path length, while displacement includes direction from start to finish. Speed is distance per time; velocity includes direction. A round trip can have a non-zero distance and zero displacement. Acceleration is change in velocity per time, so changing direction can mean acceleration even at constant speed. State units and direction consistently when comparing journeys.
Video by Cognito. The video’s own board label is retained; follow the specification reference and scope notes on this lesson for assessed content.
Viewing focus: Distinguish distance, displacement, speed and velocity
After watching, attempt these questions before opening the answers. You can also use the written lesson below.
After watching 1: What does a velocity–time gradient give?
Acceleration. Its units are m s⁻².
After watching 2: Can constant speed involve acceleration?
Yes, if direction changes. Velocity is a vector.
What you'll be able to do
Distance measures total path length, while displacement includes direction from start to finish. Speed is distance per time; velocity includes direction. A round trip can have a non-zero distance and zero displacement. Acceleration is change in velocity per time, so changing direction can mean acceleration even at constant speed. State units and direction consistently when comparing journeys.
The gradient of a distance–time graph gives speed. The gradient of a velocity–time graph gives acceleration, while the signed area under it gives displacement. A horizontal velocity–time line means constant velocity, not being stationary unless its value is zero. Area below the time axis is negative displacement; total distance adds magnitudes of separate areas. Use units to check whether you have calculated a gradient or an area.
Stopping distance is thinking distance plus braking distance. Thinking distance depends on speed and reaction time; tiredness or alcohol can increase reaction time. Braking depends on speed, tyre/road grip, braking force and vehicle conditions. Doubling speed roughly doubles thinking distance for unchanged reaction time, while braking distance often increases more strongly. A safe interpretation distinguishes measured data from an idealised constant-deceleration model.
Attempt these problems on paper before opening the worked reasoning. Explain your steps as well as giving a final answer.
Common mistakes to avoid
Key takeaways
Question 1: A velocity–time graph rises linearly from 0 to 10 m s⁻¹ over 4 s. Find displacement.
20 m.
Check the assessed scope and practical or mathematical requirements.
An external explanation or interactive activity to use alongside the lesson. It may include extension material.
Close the notes and answer from memory. Revisit any explanation you cannot yet reconstruct.
Test yourself
Answer a few questions, then review anything you missed.
Start with the quiz above to check the key ideas. You can also choose another topic from the practice library.