Ratio

Motion graphs

Connect movement, gradients and area.

Predict, test and explain

Step 1 of 3

Predict

Travel at 3 m/s for 4 seconds, then stop for 4 seconds. What is the total distance?

\text{speed}=\text{gradient}

Scroll the diagram sideways to see every label.

t=2\,\text{s}

d=6\,\text{m}

v=3\,\text{m/s}

The gradient gives speed on each straight segment. Move the time control to follow the journey; the dot above tracks distance along the journey.

Journey values
Time (s)	Distance (m)	Speed (m/s)
0	0	3
2	6	3
4	12	Changes at this instant
6	14	1
8	16	1

Explore and compare

Choose the investigation above. Predict what will change before you move a control.

Predict

Try it in the simulation. Change one thing at a time.

Explain

Notes and saved values stay in this tab. They disappear when you reload.

Hints, self-check and connections

Try a self-check

Fixed values, separate from the diagram controls.

A speed–time graph stays at 3 m/s for 8 seconds. How far does the object travel?

Hint

Find the rectangular area under the speed–time graph.

Reveal answer

24 metres. Constant speed multiplied by time gives the distance.

$d=3\times8=24\,\text{m}$

Build an explanation

Hint 1

Read the axes first. On a distance-time graph, gradient is speed: change in distance divided by change in time.

Hint 2

On a speed-time graph, gradient is acceleration. A horizontal segment means constant speed; speed zero means stationary.

Hint 3

The area under a speed-time graph gives distance travelled. Split the region into rectangles, triangles or trapeziums and include the units.

Worked example

This example uses fixed values, separate from the diagram controls.

A cyclist's speed increases uniformly from 0 m/s to 6 m/s over 3 seconds. Find the acceleration and distance travelled.

The speed-time graph is a straight line, so the acceleration is constant.
Its gradient is (6 − 0)/3 = 2 m/s².
The region under the line is a triangle with base 3 s and height 6 m/s.
Distance = ½ × 3 × 6 = 9 m. The units seconds × metres per second give metres.

Answer: Acceleration 2 m/s²; distance 9 m.

Connect this idea

Watch out: On a speed-time graph, the height is speed, the gradient is acceleration and the area is distance. The graph is not a picture of the path travelled.