PhysicsCalculating Speed from Distance and Time
Atlas stands at the finish line of a school running track, stopwatch in hand and clipboard tucked under one arm, watching two runners cross the line at different moments and jotting down numbers to compare how fast each one moved.
- Explain what speed means as a ratio of distance to time.
- Calculate average speed using the formula speed = distance ÷ time.
- Identify m/s as the SI unit for speed and km/h as a common non-SI metric unit.
- Compare the speeds of two moving objects given their distance and time data.
- Predict the distance or time of a journey when speed and one other value are known.
Key terms
- Speed
- The distance an object covers divided by the time it takes.
- Average speed
- A single number summarizing a whole trip's distance over its total time.
- SI unit
- The international standard unit, which for speed is meters per second.
- Ratio
- A comparison of two quantities by division, such as distance to time.
Speed as a Ratio
Speed is a ratio that compares distance to time by dividing one by the other. Because it is a single number, it lets you fairly compare any two moving things, even ones that covered different distances over different times. The same formula rearranges three ways: speed equals distance over time, distance equals speed times time, and time equals distance over speed. Covering up the quantity you want in a triangle shows which operation to use.
Units and Average Speed
Units must always match the numbers you used, so meters and seconds give meters per second, while kilometers and hours give kilometers per hour. Mixing meters with kilometers in one problem produces nonsense answers, so check units if a result seems impossibly large or tiny. Remember too that this formula gives average speed: it summarizes a whole journey even though a real object speeds up and slows down at different points along the way.
Worked examples
A robot travels 300 meters in 60 seconds; find its speed.
- Use speed = distance ÷ time.
- Substitute: speed = 300 m ÷ 60 s.
- Divide: 300 divided by 60 equals 5.
Answer: 5 m/s
A train travels at 90 km/h for 3 hours; how far does it go?
- Rearrange to distance = speed × time.
- Substitute: distance = 90 km/h × 3 h.
- Multiply: 90 times 3 equals 270.
Answer: 270 km
Activity
Drag each journey card onto the correct speed label by calculating speed = distance ÷ time for each one (keep track of units — some answers are in m/s, one is in km/h).
Practice
A cyclist rides 12 km in 0.5 hours; calculate the average speed in km/h.
Compare two runners who each cover 400 m but in different times.
Common mistakes to avoid
- Equal distance means equal speed.Two trips over the same distance have different speeds if they take different amounts of time.
- You multiply distance by time for speed.Speed is distance divided by time, so multiplying gives a far too large, incorrect result.
Check your understanding
A delivery robot travels 300 meters in 60 seconds. What is its speed?
A train travels at 90 km/h for 3 hours. How far does it travel?
Runner A covers 400 m in 50 s. Runner B covers 400 m in 80 s. Which statement is correct?
Recap
Speed is the ratio of distance to time, calculated with speed equals distance divided by time, and the formula rearranges to find distance or time as long as the units match and you remember it gives average speed.
Reflect
How could you use the speed formula to predict how long a journey you take regularly will last?