KS3 · Physics

Distance-time graphs

Jas's graph climbs, levels off, then drops — a hill, surely? Nope. It's Jas walking away from home, stopping at a gate, and walking back.

Jas walks to the park gate and back. Follow the dot.

02550751000306090120time (s)distance from home (m)(50, 100)

time (s): 50. distance from home (m): 100

Drag the dot along the line. At every spot ask: how far from home is Jas? And how quickly is that changing?

Watch out: This is not a drawing of the route. The line going up is not a hill and the flat bit is not flat ground. Up the side is simply how far Jas is from home.

What do you think?

The flat bit at the top

Priya's distance-time graph for a trip to the shop slopes up, stays flat for a while at 300 m, then slopes back down to 0 m. It looks a lot like a hill.

What does the flat part at 300 m show? Pick the one closest to what you think right now.
How sure are you?

Name the movement

Pick a piece of line, then pick the movement it shows.

Still to sort

Steady speed — the faster one (0)

Straight and sloping up, steeper than the other

Where the line is: Both steady sections are straight. The steeper one is faster.

Steady speed — the slower one (0)

Straight and sloping up, shallower than the other

Where the line is: Shallow and straight is slow but steady. Shallow and bending flatter is slowing down.

Stationary (0)

No change in distance

Where the line is: Stationary is a level line. A straight sloping line, however gentle, is still moving.

Moving back towards the start (0)

The distance is going down

Speeding up (0)

The steepness is increasing

Slowing down to a stop (0)

The steepness is decreasing to zero

7 of 7 still to sort.

Every piece of line on a distance-time graph tells you one kind of movement. Sort each one.

Read the scale, then calculate

Problem

Leo's distance-time graph has a straight sloping section. On the distance axis the big gridlines are 20 m apart, and each big square is split into 5 small squares. On the time axis the big gridlines are 10 s apart, also split into 5 small squares. The section starts exactly on the 10 s gridline, 3 small squares above the 40 m gridline. It ends 1 small square past the 30 s gridline, 4 small squares above the 80 m gridline. How fast is Leo going in this section?

Your turn: a journey in three phases

A bus's distance-time graph has three straight phases. Readings from the graph: at 0 s it is at 0 m; at 40 s, 200 m; at 80 s, still 200 m; at 100 s, 400 m. Find the speed in each phase, then the average speed for the whole journey.

  1. Phase 1 (0 s to 40 s): change in distance = 200 m − 0 m = 200 m; time taken = 40 s
  2. missing step
Which line is step 2?

WHAT YOU'VE LEARNED

A quick recap of today's lesson.

Height tells you how far away. Steepness tells you how fast.

What you need to know

  • Check the labels first: up the side is distance from the start, along the bottom is time.
  • Each point on the line is where the object is at that moment — its distance away, not its speed.
  • The steepness of the line is its gradient, and it shows speed: steeper means faster, shallower means slower.
  • A level line means stationary (speed zero). A line sloping down means the object is coming back towards the start.
  • A straight sloping line is a steady speed. A curve getting steeper is speeding up; a curve flattening out is slowing down to a stop.
  • speed = change in distance ÷ time taken, in m/s. For a whole journey, average speed = total distance ÷ total time.

The big picture

A distance-time graph shows how far an object is from its starting point (up the side) at each moment in time (along the bottom). Each point is a position at a time, not a speed and not a picture of the route. The steepness of the line — its gradient — shows the speed: steeper is faster, level means stationary, sloping down means moving back towards the start, and a curve means the speed is changing. You can read values off the graph and calculate speed = change in distance ÷ time taken, and the average speed for a whole journey = total distance ÷ total time.

Key points

1Find the value of one small square before reading anything: big square value ÷ number of small squares.
2Read where the object is from the line's height; read how fast it moves from the line's steepness.
3If a section doesn't start at zero, subtract the readings before you divide.
4A multi-phase journey has a separate speed for each phase — a change in gradient is a change in speed.
5Never average the phase speeds to get the journey's average speed: use total distance ÷ total time.

Worked example

Problem

A remote-control car is 90 m from its start at 10 s. Its graph is a straight line sloping downwards, reaching 30 m at 25 s. Describe what the car is doing and calculate its speed.

⚠ Watch out

Reading a distance-time graph as a picture of the route — thinking a level line is flat ground or a steady speed, and a downward line is going downhill. A level line means the object is stationary, and a downward line means it is moving back towards the start.

🧠

Memory hook

Flat — stopped. Steep — speedy. Down — coming home.

✓

Check yourself

A line sits at 20 m from 5 s to 15 s, then climbs straight to 50 m at 20 s. What is happening in each part, and how fast is the climb?

Flashcards

(13)
What does a distance-time graph show?
How far an object is from its starting point at each moment in time.
What does one point on a distance-time graph tell you?
Its position: how far away it is at that moment. It does not tell you how fast it is going.
What does the gradient (steepness) of a distance-time graph show?
The speed. The steeper the line, the faster the object is moving.
What does a level (horizontal) line show?
The object is stationary: no change in distance, so speed is zero.
What does a line sloping downwards show?
The object is moving back towards its starting point.
What does a straight sloping line show?
A constant (steady) speed.
What does a curve that gets steeper show?
The object is speeding up.
What does a curve that gets shallower until it is flat show?
The object is slowing down to a stop.
How do you find the value of one small square on a graph's scale?
Value of one big square ÷ number of small squares in it.
What is the speed equation, and what are its units?
speed = distance ÷ time, in metres per second (m/s) when distance is in metres and time in seconds.
How do you find the speed for a section that doesn't start at zero?
speed = change in distance ÷ time taken — subtract the readings first, then divide.
How do you find the average speed for a whole journey?
Total distance travelled ÷ total time taken, however many phases there are.
How do you handle a journey with several phases?
Each phase has its own gradient, so work out each phase's speed separately from its own readings.

Tap any card to flip it, or use Study as deck to go through them one at a time. In the full lesson these run as a spaced-repetition deck — you rate each card Hard, Good or Easy and the tricky ones keep coming back until they stick.

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How this lesson was checked. This KS3 Physicslesson was published through Lightbulb Learning's human-designed editorial process — the educational standards, accuracy rules and publication checks it must pass were authored and approved by Philip Halpin. It passed subject-specific assessment, automated educational checks and technical publication verification before going live (publication checks completed 30 September 2026). Published pages are monitored, human spot-checking is ongoing across the lesson library, and anything found wrong is corrected or withdrawn. How our lessons are made and checked. Spotted a mistake? Email hello@lightbulblearning.co and we'll review it.