Calculate speed from the gradient of a straightline section of a distance-time graph

What is a Distance–Time Graph?

A distance–time graph shows how far an object has travelled (on the vertical axis) as time (on the horizontal axis) passes. Each point on the graph represents the distance covered at a specific time.

Think of it like a road trip map: the y‑axis is the distance you’ve driven, and the x‑axis is how long you’ve been on the road.

How to Find Speed from a Straight‑Line Section

When the graph is a straight line, the object moves at a constant speed. The gradient (rise over run) of that line is the speed.

Mathematically:

$v = \dfrac{\Delta s}{\Delta t}$

Where $\Delta s$ = change in distance and $\Delta t$ = change in time.

📈 Analogy: Imagine driving a car on a straight highway. If you travel 120 km in 2 h, your speed is 60 km/h – exactly the slope of the distance‑time line.

Example Problem

Given the following distance–time data for a runner:

Pick any two points on the straight line, e.g., (0 s, 0 m) and (20 s, 100 m).

Compute the gradient:

$v = \dfrac{100\,\text{m} - 0\,\text{m}}{20\,\text{s} - 0\,\text{s}} = \dfrac{100}{20} = 5\,\text{m/s}$

So the runner’s constant speed is 5 m/s.

Exam Tips & Tricks

• ?? Read the question carefully. It may ask for speed, not velocity.
• ?? Choose any two points. The gradient is the same anywhere on a straight line.
• ?? Check units. Distance in metres, time in seconds → speed in m/s.
• ?? Look for “constant speed” clues. A straight line means no acceleration.
• ?? Use a calculator if needed. But many questions allow simple division.

📝 Remember: The gradient of a distance–time graph is the speed. No need to over‑think!