Distance-Time Graphs Explained: KS3 Maths

A distance-time graph shows how far an object has travelled from a starting point over time. Time runs along the horizontal axis and distance along the vertical axis. The gradient (steepness) of the line equals the object's speed: a steeper line means faster travel; a flat line means the object is stationary.

What does each part of a distance-time graph tell you?

Each segment of the graph carries specific meaning:

Segment | What it looks like | What it means
Sloping upward | Line going up-right | Moving away from start
Flat (horizontal) | Horizontal line | Stationary — at rest
Sloping downward | Line going down-right | Returning towards start
Steeper slope | Same time, more distance | Faster speed

How do you calculate speed from a distance-time graph?

Speed is calculated using the gradient of the line:

Speed = distance ÷ time

On the graph, pick two clear points on a straight segment and read off their coordinates. Then apply:

Speed = (change in distance) ÷ (change in time)

Always state the units (e.g. km/h or m/s) — they come from dividing the distance unit by the time unit.

Worked example: reading a distance-time graph

A cyclist leaves home and the graph shows three segments:

Segment A: from 0 to 30 minutes, distance increases from 0 km to 15 km.

Segment B: from 30 to 45 minutes, distance stays at 15 km (flat line).

Segment C: from 45 to 75 minutes, distance decreases from 15 km back to 0 km.

Calculating speeds:

Segment A: 15 km ÷ 0.5 h = 30 km/h

Segment B: distance change = 0, so speed = 0 km/h (stationary).

Segment C: 15 km ÷ 0.5 h = 30 km/h (same speed, returning home).

Note: the direction is shown by the line going downward in Segment C — the cyclist is heading back, but the calculated speed (magnitude) is still 30 km/h.

What does a curved line mean on a distance-time graph?

A straight line means constant speed; a curve means the speed is changing (accelerating or decelerating). On a curve, the gradient at any instant is the instantaneous speed at that point. At KS3, you mainly deal with straight-line segments; curves appear more often at GCSE, where you may estimate the instantaneous speed by drawing a tangent to the curve.

How do you read the total distance travelled?

Add up the distances covered in each segment — not just the final distance from the start. In the cyclist example:

Segment A: 15 km (away)

Segment B: 0 km

Segment C: 15 km (back)

Total distance travelled: 30 km

The displacement (straight-line distance from start) at the end is 0 km, because the cyclist returned home. Distance and displacement are different — know which one the question asks for.

What common mistakes should you avoid?

Confusing displacement with total distance: A return journey may end at 0 km displacement but covers real total distance.

Ignoring units: Always convert time to the same unit throughout (e.g. all in hours or all in minutes).

Reading a flat line as "no distance": A flat line means no change in distance — the object is stopped, not at zero distance.

Forgetting that a steeper downward slope is still a speed, not a negative speed: At KS3, speed is always positive; direction is shown by whether the line goes up or down.

Frequently asked questions

What does the gradient of a distance-time graph represent?

The gradient represents the object's speed at that point. A steeper gradient means a higher speed. Calculate it by dividing the change in distance (vertical) by the change in time (horizontal) over any straight segment.

How can you tell when an object is stationary?

The line is horizontal — perfectly flat. Distance is not changing, so the object has stopped. Any time period showing a flat line is a rest period; its duration is the length along the time axis.

Can the line on a distance-time graph go backwards below zero?

The distance axis shows how far from the starting point the object is, so it cannot go below zero in a standard distance-time graph. If the object returns past the starting point, distance resets or the graph may use "position" instead — that is a displacement-time graph, where negative values are allowed.

What is the difference between speed and velocity on these graphs?

Speed is how fast the object is moving (always positive). Velocity also includes direction (positive or negative). A distance-time graph shows speed — the line cannot go negative. A displacement-time graph shows velocity when the line dips below zero (object moving in the opposite direction).

For Socratic maths practice with graphs and motion, see aitutors.me.