Mario drives from his home to his friend’s house. He watches a movie at his friend’s house and then drives home.
Which distance−time graph best represents Mario’s complete journey?
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The travel graph shows the distance of a runner from a town.
Between what times was the runner travelling at their greatest speed?
- 10 am and 11 am
- 11 am and 11:30 am
- 11:30 am and 1 pm
- 1 pm and 2:30 pm
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The distance-time graph shows the first two stages of a car journey from home to a holiday house.
- At what speed, in kilometres per hour, did the car travel during stage \(A\) of the journey? (1 mark)
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- For how long did the car stop during stage \(B\) of the journey? (1 mark)
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- After stage \(B\), the car continues to travel towards the holiday house at a constant speed of \(50\ \text{km/h}\) for 2 hours. Graph this part of the journey on the grid above. (2 marks)
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Show Answers Only
a. \(100\text{ km/h}\)
b. \(30\text{ minutes}\)
c.
Show Worked Solution
a. \(S=\dfrac{D}{T}=\dfrac{150}{1.5}=100\ \text{km/h}\)
b. \(\text{Stage}\textit{ B}=1.5\rightarrow 2\text{ hours}=30\text{ minutes}\)
c. \(\text{Position after 2 hours at 50km/h}=(150+2\times 50 , 2 + 2) = (250 , 4)\)
♦ Mean mark (c) 50%.
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The travel graph displays Jamie's trip which began at town `M` at 8 am and finished at town `N`.
- How far apart are the two towns? (1 mark)
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- At what time during the day did Jamie arrive back at town `M` ? (1 mark)
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- What was the total distance that Jamie travelled? (1 mark)
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- Between which times in the day was Jamie travelling at the fastest speed? Justify your answer, without calculations. (2 marks)
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Sue walks along a trail, starting at 7 am and finishing at 10 am. The travel graph shows Sue’s journey from the start to the finish. The journey has been broken into six sections, `A`, `B`, `C`, `D`, `E` and `F`.
- On two occasions Sue stopped to rest. In which sections of the journey did Sue rest? (1 mark)
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- In which section of the journey did Sue travel fastest? Justify your answer. (2 marks)
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- Kim walked along the same trail, also starting at 7 am and finishing at 10 am. Kim walked at a constant speed for the entire journey.
- By showing Kim’s journey on the grid above, determine between what times Sue was ahead of Kim. (3 marks)
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- `B\ text(and)\ E`
- `text(S)text(ection)\ C.\ text(Slope is the steepest.)`
- `text(8:30 am – 9:15 am)`
Show Worked Solution
a. `B\ text(and)\ E`
♦ Mean mark part (b) 44%.
b. `text(Fastest travel occurs when the slope is the steepest.)`
♦♦ Mean mark part (c) 30%.
`:. text(S)text(ection)\ C`
c.
`text(Sue was ahead when her graph is higher than Kim’s.)`
`:.\ text(She was ahead between 8:30 am – 9:15 am)`
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The travel graph displays Nikau's car trip along a straight road from home and back again. The trip has been broken into four separate sections: `A`, `B`, `C` and `D`.
- How far did Nikau travel in total? (1 mark)
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- In which section of the trip, `A`, `B`, `C` and `D`, did Nikau travel the fastest? (1 mark)
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