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Graphs
Example 1
David went to Eva's house to borrow her notes. While he was walking, he bought an ice cream. The following graph shows his movement.
- Make a table based on the graph. Where and when did David stop?
- How many \latex{ minutes } did it take him to get back home?
- Where did he walk the fastest? What distance did he cover in each section \latex{ per\; minute? }
\latex{ distance\, from\, the\, house }
\latex{ time \,passed }
\latex{ (min) }
\latex{ (m) }
\latex{ 450 }
\latex{ 400 }
\latex{ 350 }
\latex{ 300 }
\latex{ 250 }
\latex{ 200 }
\latex{ 150 }
\latex{ 100 }
\latex{ 50 }
\latex{ 2 }
\latex{ 4 }
\latex{ 6 }
\latex{ 8 }
\latex{ 10 }
\latex{ 12 }
\latex{ 14 }
\latex{ 16 }
\latex{ 18 }
\latex{ 20 }
\latex{ 22 }
\latex{ 24 }
\latex{ A }
\latex{ B }
\latex{ C }
\latex{ D }
\latex{ E }
\latex{ F }
Solution
- Write the time passed in the first row, the distance from David's house in the second, and the places where he stopped in the third.
time passed
\latex{(min)}
\latex{(min)}
distance
\latex{(m)}
\latex{(m)}
stops
\latex{ 2 }
\latex{ 4 }
\latex{ 6 }
\latex{ 8 }
\latex{ 10 }
\latex{ 12 }
\latex{ 14 }
\latex{ 16 }
\latex{ 18 }
\latex{ 20 }
\latex{ 22 }
\latex{ 24 }
\latex{ 100 }
\latex{ 200 }
\latex{ 300 }
\latex{ 300 }
\latex{ 300 }
\latex{ 350 }
\latex{ 400 }
\latex{ 400 }
\latex{ 400 }
\latex{ 400 }
\latex{ 200 }
\latex{ 0 }
ICE CREAM
PARLOUR
PARLOUR
EVA’S HOUSE
- It took David \latex{ 24 \;minutes } to get back home.
David walked the fastest between points \latex{ E } and \latex{ F }. This is when he covered the largest distance per minute.
Between points \latex{ A } and \latex{ B } | he covered \latex{ 300\, m } in \latex{ 6\, minutes }, so he covered \latex{ 50\,m } in \latex{ 1\,minute }. | |
Between points \latex{ B } and \latex{ C } | he covered \latex{ 0 \,m } in \latex{ 4 \,minutes } (buying ice cream). | |
Between points \latex{ C } and \latex{ D } | he covered \latex{ 100\, m } in \latex{ 4\, minutes, } so he covered \latex{ 25\, m } in \latex{ 1 \,minute }. | |
Between points \latex{ D } and \latex{ E } | he covered \latex{ 0\, m } in \latex{ 6 \,minutes } (at Eva’s house). | |
Between points \latex{ E } and \latex{ F } | he covered \latex{ 400 \,m } in \latex{ 4 \,minutes }, so he covered \latex{ 100 \,m } in \latex{ 1 \,minute }. | |
David walked the fastest between points \latex{ E } and \latex{ F }. This is when he covered the largest distance \latex{ per\; minute. }
Exercises
{{exercise_number}}.
- Peter and his friends went to the cinema. Everybody bought a bag of popcorn, which they ate during the film. The following graphs show the amount of popcorn left in the bag as time passed. Write down what happened.
Peter
Matt
Greg
Frank
time
time
time
time
height of popcorn
in the bag
in the bag
height of popcorn
in the bag
in the bag
height of popcorn
in the bag
in the bag
height of popcorn
in the bag
in the bag
– What does it mean if the graph is steeper than before?
– What does the horizontal line on Frank’s graph mean?
– Who finished the bag of popcorn first?
– How should you eat the popcorn to get a horizontal line segment?
– Greg's graph does not start from the vertical axis. Why not?
- Tom and Tamara went to the cinema. Both of them bought a bag of popcorn. Tom was very hungry, so he ate half of the bag fast, stopped for a while, and later continued eating his popcorn at the same pace. Tamara waited a few minutes, then started to eat the popcorn at a uniform pace. When she saw that Tom had almost eaten the entire bag, she offered him some of her popcorn. This way, both of them could finish their bags of popcorn at the same time.
– Use different colours in the same coordinate system to represent the amount of Tom's and Tamara's popcorn as a function of time.
– How do you represent that Tom ate half of his popcorn?
– How do you represent that, after the break, Tom continued eating his popcorn at the same pace as before?
– How do you represent that Tamara gave some of her popcorn to Tom?
– How do you represent that they finished their bags of popcorn at the same time?
– How do you represent that Tom ate half of his popcorn?
– How do you represent that, after the break, Tom continued eating his popcorn at the same pace as before?
– How do you represent that Tamara gave some of her popcorn to Tom?
– How do you represent that they finished their bags of popcorn at the same time?
{{exercise_number}}. Each of the four graphs shows the movement of two vehicles. Which one shows that
- the vehicles started moving at the same time;
- one of them covered a larger distance than the other during the same amount of time;
- the vehicles did not start from the same place;
- one of them passed the other?
1.
2.
4.
3.
distance
distance
distance
distance
time
time
time
time
\latex{ A }
\latex{ B }
\latex{ C }
\latex{ D }
\latex{ G }
\latex{ H }
\latex{ E }
\latex{ F }
{{exercise_number}}.
Petra and her father left home at the same time. They walked together for \latex{ 10 \;minutes }, then said goodbye to each other and started walking in different directions. Petra arrived at school in \latex{ 10 \;minutes }, while her father arrived at his workplace in \latex{ 15 \;minutes }. Does line \latex{ 1 } or \latex{ 2 } represent Petra's trajectory? Make two separate tables about Petra's and her father's movements. What does it indicate that line \latex{ 2 } is steeper?
distance
(m)
(m)
time (minutes)
\latex{ 3,000 }
\latex{ 2,500 }
\latex{ 2,000 }
\latex{ 1,500 }
\latex{ 1,000 }
\latex{ 500 }
\latex{ 5 }
\latex{ 10 }
\latex{ 15 }
\latex{ 20 }
\latex{ 25 }
\latex{ 30 }
\latex{ 2. }
\latex{ 1. }
Quiz
Grandma walked to the park, sat down for a while, and then went home. Which graph shows the distance covered, and which one shows the distance from her house?
1.
2.
time
time
