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3 Ratios, rates, and time
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AustraliaNSW
Stage 4

3.06 Travel graphs

Lesson
Worksheet
Practice
Lesson

Travel graphs

Travel graphs are used to show an object's change in distance over time. The horizontal axis shows time and the vertical axis shows distance.

We can determine how fast something is going based on how steep the line is. If a certain part of the line is very steep then the object is moving faster. If the line is going horizontally, then time is passing but the distance isn't changing, which means that the object isn't moving. If the line is sloping down this means the object is travelling back to the origin.

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\text{Time (mins)}
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\text{Distance from school (km)}

Consider the travel graph of a student being driven away from school. The distance is given in relation to the school. So the starting disance of 0 km away from school means that they are at school.

The student is driven away from school in the first line shown. The line then gets steeper, so the student is travelling faster away from school. At the 5 minute mark the car stops moving for 2 minutes, shown by the horizontal line. The car then starts travelling back towards school.

Travel graphs show how far an object is from a point, and how that changes over time. It also shows how fast an object might be moving based on the distance it has travelled in a that amount of time.

Examples

Example 1

Paul is driving his child home from school. After 5 minutes, the car slows down. Which travel graph represents this journey?

A
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\text{Time (mins)}
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\text{Distance from school (km)}
B
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\text{Time (mins)}
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\text{Distance from school (km)}
C
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\text{Time (mins)}
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\text{Distance from school (km)}
D
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\text{Time (mins)}
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\text{Distance from school (km)}
Worked Solution
Create a strategy

The steeper the line the faster the speed of the travel. So after 5 minutes the line should be less steep.

Apply the idea

Option B is the graph that represents the car slowing down after 5 minutes since the line before 5 minute mark is steeper than the line after that.

Example 2

The Weber family travel 600 km every year for their annual holidays. Their distance from home on the trip this year is given in this travel graph:

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\text{Time (hours)}
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\text{Distance from home (km)}
a

When did they stop for a break?

A
1 hour into the journey
B
5 hours into the journey
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4 hours into the journey
D
2 hours into the journey
Worked Solution
Create a strategy

A horizontal line indicates no movement or change in distance, so this will be when they stopped for a break.

Apply the idea

The Weber family stopped 2 hours into the journey which is when the horizontal line starts. The correct option is D.

b

How far from their destination were they after 2 hours?

Worked Solution
Create a strategy

Find the distance travelled after 2 hours and subtract it from the total distance.

Apply the idea

The Weber family has travelled 200 km after 2 hours.

\displaystyle \text{Distance}\displaystyle =\displaystyle 600-200Subtract 200 from 600
\displaystyle =\displaystyle 400 \text{ km}Evaluate
c

What are the two time periods when they were travelling at the same speed?

Worked Solution
Create a strategy

Look for two line segments that have the same steepness.

Apply the idea

The period where the line has the same steepness or slope are the first 2 hours and the final 3 hours. So this is when they were travelling at the same speed.

Idea summary

Travel graphs show how far an object is from a point, and how that changes over time. It also shows how fast an object might be moving based on the distance it has travelled in a that amount of time.

Outcomes

MA4-11NA

creates and displays number patterns; graphs and analyses linear relationships; and performs transformations on the Cartesian plane

MA4-15MG

performs calculations of time that involve mixed units, and interprets time zones

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