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Measurement, STD2 EQ-Bank 20

The travel graph displays Jamie's trip which began at town `M` at 8 am and finished at town `N`.
 

   

  1. How far apart are the two towns?   (1 mark)

  2. At what time during the day did Jamie arrive back at town `M` ?   (1 mark)

  3. What was the total distance that Jamie travelled?   (1 mark)

  4. Between which times in the day was Jamie travelling at the fastest speed? Justify your answer, without calculations.   (1 mark)

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a.   `140\ text{km}`

b.   `10\ text{am}`

c.    `220\ \text{km}`  

d.    `\text{Between 11 – 11:30 am}`

Show Worked Solution

a.   `140\ text{km}`
 

b.   `text{James arrives back at town when he is 140 km away (2nd time).}`

`=> 10\ text{am}`
 

c.    `\text{Total Distance} = 40 + 40 + 60+ 80=220\ text{km}` 
  

d.   `text{Fastest speed → graph is the steepest (either up or down)}`

`:.\ text{Fastest speed between 11 – 11:30 am}`

Measurement, STD2 EQ-Bank 27

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`.
 

     

  1. In which section of the journey did Sue travel fastest? Justify your answer.   (2 marks)

  2. 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.
  3. By showing Kim’s journey on the grid above, determine between what times Sue was ahead of Kim.   (3 marks)

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a.    `text(S)text(ection)\ C\ \text{(Slope is the steepest)}.`

b.    `text(8:30 am – 9:15 am)`
 
           

Show Worked Solution

a.   `text{Fastest travel occurs when the slope is the steepest.}`

`=>\ text{Section}\ C`

b.

`text(Sue was ahead when her graph is higher than Kim’s.)`

`:.\ text(She was ahead between 8:30 am – 9:15 am)`

Measurement, STD2 EQ-Bank 32

The distance-time graph shows the first two stages of a car journey from home to a holiday house.
  

  1. At what speed, in metres per second, did the car travel during stage \(A\) of the journey? Give your answer correct to one decimal place.   (2 marks)
  2. 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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a.    \(27.8\ \text{m/s}\)

b.   

Show Worked Solution

a.   \(\text{Distance travelled} = 150\ \text{km}\ =150\,000\ \text{m}\)

\(\text{Stage A duration = 1.5 hours}\)

\(\text{Express 1.5 hours in minutes:}\)

\(\text{Minutes} = 1.5 \times 60 \times 60 = 5400\ \text{seconds}\)

\(\text{Speed} = \dfrac{150\,000}{5400}=27.77…=27.8\ \text{m/s}\)

 

b.    \(\text{Position after 2 hours at 50km/h}=(150+2\times 50 , 2 + 2) = (250 , 4)\)
 

   

Measurement, STD2 EQ-Bank 2 MC

The travel graph shows the distance of a runner from a town.
 

Between what times was the runner travelling at their greatest speed?

  1. 10 am and 11 am
  2. 11 am and 11:30 am
  3. 11:30 am and 1 pm
  4. 1 pm and 2:30 pm
Show Answers Only

\(A\)

Show Worked Solution

\(\text{Greatest speed is when the graph is steepest.}\)

\(\therefore\ \text{Greatest speed occurs between 10 am and 11 am.}\)

\(\Rightarrow A\)