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Middle Years

12.04 Distance time graphs

Worksheet
Distance time graphs
1

Sketch a graph that shows the height of a ball being thrown vertically into the air. Time should be on the horizontal axis, and height should be on the vertical axis.

2

A man is driving along a highway in a car at a constant speed. After a period of time, he decreases his speed because of road work. Sketch a graph that represents the relationship between distance travelled and time taken.

3

Tina is cycling to the bus stop, but halfway there she gets a flat tire and has to push her bike the rest of the way. Upon reaching the bus stop, she has a short wait for the bus and then catches the bus to her final destination. Sketch a graph that represents the relationship between distance travelled and time taken.

4

Which line segment of this travel graph is impossible? Explain your answer.

3\text{ pm}
4\text{ pm}
5\text{ pm}
\text{Time}
1\text{ km}
2\text{ km}
3\text{ km}
4\text{ km}
5\text{ km}
6\text{ km}
\text{Distance}
5

Ben travels forwards and backwards along a straight line. The graph shows Ben's distance from his starting point at various times of the day:

9:00
10:00
11:00
12:00
13:00
14:00
15:00
16:00
17:00
\text{Time}
50\text{ km}
100\text{ km}
150\text{ km}
200\text{ km}
250\text{ km}
300\text{ km}
\text{Distance}
a

How far did Ben travel by 11 am?

b

What happened to Ben's speed at 11 am?

c

Evaluate Ben's speed between 11 am and 1 pm.

d

What distance did Ben travel between 1 pm and 2 pm?

e

What is the furthest distance travelled from the starting point?

f

What is the total distance travelled by Ben from 9 am to 4 pm?

6

Ken starts travelling at 9 am from point A to point B. The distance between Ken and point B at various times in his journey is shown on the graph below:

9:00
10:00
11:00
12:00
13:00
14:00
15:00
16:00
17:00
\text{Time}
20\text{ km}
40\text{ km}
60\text{ km}
80\text{ km}
100\text{ km}
120\text{ km}
\text{Distance}
a

How far is point B from point A?

b

How many hours was Ken's journey from point A to point B?

c

State the time period in which Ken travelled at the fastest speed.

d

Find Ken's fastest speed in \text{km/h}.

e

Find the distance in kilometres travelled by Ken between 1:30 pm and 4 pm.

f

Find the total distance travelled by Ken from 9 am to 4 pm.

7

The following graph describes Frank's distance from home throughout his journey:

a

How far was Frank from home when he started driving at 5 am?

b

How far was he from home by 7 am?

c

How long did he rest for?

d

How far did he travel between 7 am and 9 am?

e

Was Frank travelling faster in the first two hours or the last two hours of his trip?

1
2
3
4
5
6
7
8
9
10
\text{Time (am)}
10
20
30
40
50
60
\text{Distance (km)}
8

Consider the following travel graph:

8:00
9:00
10:00
11:00
12:00
13:00
14:00
15:00
16:00
17:00
\text{Time}
5
10
15
20
25
30
35
\text{Speed (km/h)}
a

Find the total time taken for the journey.

b

Find the total distance covered in the journey.

c

Find the average speed during the journey, correct to two decimal places.

9

The graph represents Beth's distance from home over a 9-minute interval:

a

When she first started to move, did she travel towards or away from home?

b

For how many minutes did she stay home?

c

How many minutes into her journey was she when she left home?

d

Find Beth's furthest distance from home.

e

How long, from the time she left home, did it take for Beth to return home?

f

Find the total distance she travelled over the 9-minute period.

1
2
3
4
5
6
7
8
9
10
11
\text{Time (min)}
1
2
3
4
5
\text{Distance (km)}
10

The following travel graph shows the distance covered by Neil on his journey versus time. Neil took two trips and rested between them.

a

Find the average speed of the first trip.

b

Find the average speed of the second trip.

c

Find the average speed of the entire journey.

2
4
6
8
10
12
14
\text{Time (min)}
2
4
6
8
10
12
14
\text{Distance (km)}
11

The graph shows a train’s distance from the central station throughout the day:

9:00
10:00
11:00
12:00
13:00
14:00
15:00
16:00
\text{Time}
20\text{ km}
40\text{ km}
60\text{ km}
80\text{ km}
100\text{ km}
120\text{ km}
140\text{ km}
160\text{ km}
180\text{ km}
200\text{ km}
\text{Distance}
a

When did the train change direction and start travelling back towards the central station?

b

At what time did the train stop to change drivers?

c

How far had the train travelled between 12 pm and 1 pm?

d

How far had the train travelled between 10 am and 4 pm?

e

Between which times was the train was travelling fastest?

12

The graph shows a traveller's distance from home each hour:

9:00
10:00
11:00
12:00
13:00
14:00
15:00
16:00
\text{Time}
50
100
150
200
250
300
\text{Distance (km)}
a

At what speed was the person travelling between 11:00 am and 1:00 pm?

b

In which interval of time was the person travelling fastest?

c

What does the horizontal interval on the graph represent?

13

This line graph shows the distance Buzz was from his house as he travelled to visit his grandparents:

a

How far was Buzz from his house at 10:30 am?

b

What time did Buzz get back home?

c

What was the furthest distance Buzz was from his house?

10:00
11:00
12:00
13:00
\text{Time}
1
2
3
4
5
\text{Distance (km)}
14

Edward walks from his home to school on occasion. The graph represents his distance from school over one particular journey:

a

How far away is Edward's home from his school?

b

How long does Edward take to get to school?

c

How far is Edward from his school after 10 minutes?

d

How long did he have left in his trip when he was 1200 \text{ m} away from his school?

10
20
30
40
50
\text{Time (min)}
250
500
750
1000
1250
1500
1750
2000
2250
\text{Distance (m)}
15

During a test drive of an expensive car, the car’s distance from the car dealership was tracked. The graph below shows how the distance changed over time:

a

How long did the test drive take?

b

In which two 10-minute intervals was the driver travelling at the same speed?

10
20
30
40
50
60
\text{Time (min)}
2
4
6
8
10
12
14
16
18
20
22
\text{Distance (km)}
16

Write a story to describe the following travel graphs:

a
b
17

Mr. and Mrs. Weber and their family travel 270 \text{ km} every year for their family trip. The following graph shows the travel distance and time:

a

If the family leaves at 3 am, what time would they arrive at their destination?

b

How far had they travelled after 5 hours?

c

During the drive, the family stops for breakfast. At what time do they stop?

d

At what times did their speed decrease?

e

The neighbours, the Axelrod family, have decided to join the Weber family on this trip but will drive there separately. For the Axelrod family's trip:

  • They leave at the same time as the Weber family, but drive slower at first.

  • They increase speed after 2 hours.

  • They only stop for breakfast for half an hour.

  • They arrive at the destination at the same time.

Sketch a graph showing both the Webers' trip and the Axelrods' trip.

1
2
3
4
5
6
7
\text{Time (hr)}
30
60
90
120
150
180
210
240
270
300
\text{Distance (km)}
Graph comparisons
18

The graph shows the progress of two competitors in a cycling race, where distance is in kilometres and time is in hours:

Who is travelling faster and by how much?

1
2
3
4
5
6
7
8
\text{Time}
50
100
150
200
250
300
\text{Distance}
19

The graph shows the progress of two competitors in a cycling race, where distance is in kilometres and time is in hours:

Who is travelling faster and how much faster is he travelling?

1
2
3
4
5
6
\text{Time}
25
50
75
100
125
150
175
200
\text{Distance}
20

A husband and wife exercise each day for 20 minutes before dinner. The wife walks briskly, while the man runs. The distance each of them travel is shown on the graph:

a

Find the difference in distance that each of them covers after 20 minutes.

b

Find the distance the wife covers each minute.

c

Find the distance the husband covers each minute.

d

How long would it take the wife to walk the same distance that her husband runs in 6 minutes?

4
8
12
16
20
24
\text{Time (min)}
400
800
1200
1600
2000
2400
2800
3200
3600
4000
4400
\text{Distance (m)}
21

Two students were walking on a straight walking track and their travel graph is plotted:

a

How far did Student A walk?

b

How many more metres did Student A walk than Student B during the first 5 minutes?

c

What is the average speed of Student A in metres per minute?

d

What is the average speed of Student B in metres per minute?

e

Assuming Student A and Student B walk at these speeds to complete the 2 \text{ km} track on the field, how many minutes longer would Student B take than Student A?

1
2
3
4
5
6
\text{Time (min)}
50
100
150
200
250
\text{Distance (m)}
22

The travel graph of John and Kate is shown below:

a

Calculate the difference in the amount of time travelled for John and Kate.

b

Calculate John's average speed in \text{km/h} for the trip. Round your answer to two decimal places.

c

Calculate Kate's average speed in \text{km/h} for the trip.

d

At what time had Kate and John travelled the same distance?

e

At the time when Kate and John had travelled the same distance, what was the actual distance travelled?

9:00
10:00
11:00
12:00
\text{Time}
5
10
15
20
25
30
35
\text{Distance (km)}
23

Sourav and Irena transport medical equipment from their respective work sites throughout the day. The graph shows their distance from home:

11:00
12:00
13:00
14:00
15:00
16:00
17:00
18:00
\text{Time}
50\text{ km}
100\text{ km}
150\text{ km}
200\text{ km}
250\text{ km}
300\text{ km}
350\text{ km}
\text{Distance}
a

If they are at their respective worksites at the beginning of the day, how far apart are their worksites?

b

At what time are both Sourav and Irena the same distance away from their respective work sites?

c

How far apart are they at 1 pm?

d

At what time is Sourav 25 \text{ km} from arriving at his office?

e

How long after Sourav returned to his worksite did Irena return to hers?

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