Speed, velocity & acceleration
The idea
You already know how to say where something is and that objects move from place to place. Speed puts a number on that motion: speed = distance ÷ time, so a runner covering 100 m in 20 s moves at 5 m/s. Velocity is speed with a direction attached — 5 m/s north is a different velocity from 5 m/s south, even though the speedometer reading is identical. That direction matters whenever you care where something ends up, not just how fast it got there.
Acceleration measures how quickly velocity changes: acceleration = change in velocity ÷ time, with units of m/s². The common trap is thinking acceleration only means speeding up. Slowing down is acceleration too (the velocity is changing), and so is turning at constant speed, because the direction part of velocity is changing. A useful habit: whenever you read m/s², say it as 'meters per second of speed gained or lost, every second' — it turns an abstract unit into a story about the motion.
Worked example
A cyclist rides 120 m down a straight street in 20 s at a steady pace. Then she sprints, going from 6 m/s to 10 m/s in 2 s. Find her steady speed and her acceleration during the sprint.
- Start with the steady stretch: speed = distance ÷ time = 120 m ÷ 20 s = 6 m/s. That means she covers 6 meters during every second of that stretch.
- For the sprint, find how much the velocity changed: 10 m/s − 6 m/s = 4 m/s of extra speed gained.
- Divide the change by the time it took: acceleration = 4 m/s ÷ 2 s = 2 m/s². In words, she gains 2 m/s of speed during each second of the sprint.
- Sanity-check by replaying the sprint: starting at 6 m/s, after one second she is at 8 m/s, and after two seconds she is at 10 m/s — exactly the final speed given, so the numbers hang together.
Answer. Her steady speed is 6 m/s, and her sprint acceleration is 2 m/s².
Check your understanding
- Why is a car driving around a curve at a perfectly constant 30 km/h still accelerating?
- How would you explain to a friend when the difference between speed and velocity actually matters, using a trip they take every day?
- What does a negative acceleration tell you about a motion, and why does it not always mean the object is moving backward?
- Two runners finish a race with the same average speed — in what different ways could their motion during the race have looked?
Build the foundations first
Speed, velocity & acceleration builds on these concepts. If any feel shaky, start there.