Distance-time graphs show distance on the vertical axis and time on the horizontal axis.

The gradient of a distance-time graph represents speed because gradient =

The speed is .

The gradient of a distance-time graph represents speed.

When displaying a journey, the vertical axis will often represent the distance from a particular place rather than the distance travelled. Such graphs are known as displacement-time graphs.

Sections A and C show travelling away from home.

Sections B and D are when the journey has paused for a rest or a wait. Section E shows the return home.

- Question
What is the speed in section A?

Speed = gradient = = 3 miles per hour.

- Question
What is happening in section B?

They stopped for 30 minutes (0.5 hours) between 9:00 and 9:30.

- Question
What is the average speed between 8:00 and 11:00?

Speed = gradient =

Average speed = miles per hour.

**Note**: We must use the total change in distance and the total change in time. A common error is to find the average of the speeds for sections A, B and C.

- Question
What is the total distance travelled?

16 miles: 8 miles there and 8 miles back.

- Question
What is the speed in section E?

Gradient =

The speed is 8 miles per hour.

The gradient in section E is -8.

The speed is 8 miles per hour because speed is always a positive value. The velocity, however would be -8 miles per hour because the sign indicates direction (with a positive value meaning travelling away from home and negative value meaning travelling towards home).