Speed, Velocity, and Reading a Distance-Time Graph
Lumi crouches at the start line of a sunny school track, holding a stopwatch and a tablet that draws a distance-time graph as a jogger runs past flag markers
- Calculate speed by dividing the distance traveled by the time taken.
- Distinguish between speed (how fast) and velocity (speed plus direction).
- Interpret a distance-time graph, identifying when an object moves fast, slow, or stays still.
- Predict how far a moving object will travel after a given amount of time using its speed.
Key terms
- Speed
- How fast something moves, found by dividing distance traveled by time taken.
- Velocity
- Speed together with a direction of travel, such as 2 m/s north.
- Distance-time graph
- A graph with time across the bottom and distance up the side showing motion.
- Slope
- The steepness of a line on the graph, which represents the object's speed.
Speed Versus Velocity
Speed is a single number that tells you only how fast something is going. Velocity carries an extra piece of information — the direction — so it fully describes the motion. Two objects can share an identical speed yet have completely different velocities if they head in different directions. This is why a runner who jogs 5 m/s east and one who jogs 5 m/s west are matched in speed but opposite in velocity, and over time they drift far apart.
Reading the Slope
On a distance-time graph the steepness of the line, called the slope, directly shows the speed. A steeper line covers more distance in the same time, so it represents a faster object. A flat horizontal line covers no distance as time passes, meaning the object is standing still. By comparing slopes you can rank several objects from slowest to fastest without doing any arithmetic, just by looking at which line climbs most steeply.
Worked examples
A car travels 150 meters in 30 seconds; find its speed.
- Use speed = distance ÷ time.
- Substitute: speed = 150 m ÷ 30 s.
- Divide: 150 divided by 30 equals 5.
Answer: 5 m/s
A walker moves at 3 m/s for 12 seconds; how far does she travel?
- Rearrange to distance = speed × time.
- Substitute: distance = 3 m/s × 12 s.
- Multiply: 3 times 12 equals 36.
Answer: 36 meters
Activity
Order these distance-time graph segments from the slowest mover to the fastest mover.
Practice
A skater covers 60 meters in 12 seconds; calculate the skater's speed in m/s.
Explain why two trains at the same speed can still have different velocities.
Common mistakes to avoid
- Speed and velocity mean the same thing.Velocity always includes a direction, while speed is only the size of the motion with no direction attached.
- A flat line on the graph means fast motion.A flat horizontal line means distance is not changing, so the object is actually stopped, not moving fast.
Check your understanding
A runner travels 100 meters in 20 seconds at a steady pace. What is the runner's speed?
On a distance-time graph, what does a flat (horizontal) line tell you about the object?
Two delivery vans each drive at 40 km/h, but one goes east and the other goes west. A student says they have the same velocity. Is the student correct?
A cyclist rides at a steady 4 meters per second. How far will the cyclist travel in 15 seconds?
Recap
Speed is distance divided by time, velocity adds a direction, and on a distance-time graph a steeper slope means faster motion while a flat line means the object has stopped.
Reflect
When might knowing only an object's speed, without its direction, leave you unable to predict where it ends up?