Gradient Detective

Gradient Detective 🕵️

A **distance–time graph** hides a whole journey inside a line. Your job as a detective is to read the **gradient** — because on this graph the gradient IS the **speed**. Steep means fast, gentle means slow, flat means stopped. Learn to read those clues and you can describe any journey from its graph.

Reading a distance–time graph 📉

On a distance–time graph: • **Time** runs along the horizontal axis, **distance** up the vertical axis. • The **gradient** of the line (distance ÷ time) gives the **speed**. A line rising steeply covers a lot of distance in little time — a high speed. A gently rising line is slow.

Steep, gentle, flat, down 🧭

Four clues to memorise: • **Steep upward** line → moving away **fast**. • **Gentle upward** line → moving away **slowly**. • **Flat (horizontal)** line → **stopped** (distance not changing). • **Downward** line → **returning** towards the start.

What does flat mean?

On a distance–time graph, what does a horizontal (flat) section tell you?

• The object is stopped — its distance is not changing
• It is moving at a steady, constant speed
• It is moving very fast
• It is returning to the start

A car journey 🚗

Here is the journey shown on the graph coming up (distance in km, time in hours): • **0–1 h:** 0 → 60 km (a steady drive out). • **1–2 h:** stays at 60 km (a stop). • **2–3 h:** 60 → 180 km (a fast stretch). • **3–5 h:** 180 → 0 km (the drive home).

Find the fastest section

An interactive activity.

Speed on the way out

An interactive activity.

Speed on the fast stretch

An interactive activity.

Spot the return journey

Which part of the graph shows the car driving back towards the start?

• The section that slopes downwards, back to zero distance
• The flat, horizontal section
• The steepest upward section
• The gentle upward section

Match each line to what it means

Order the method

An interactive activity.

The detective rules

On a distance–time graph, the gradient of a line gives the _____. A horizontal (flat) section means the object is _____. A line sloping back down towards the time axis shows the object _____ to its start.