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 .
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.
What is the speed in section A?
Speed = gradient = = 3 miles per hour.
What is happening in section B?
They stopped for 30 minutes (0.5 hours) between 9:00 and 9:30.
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.
What is the total distance travelled?
16 miles: 8 miles there and 8 miles back.
What is the speed in section E?
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).