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Ambrose drives at 50 km/h for 2 hours, rests for 1 hour, and then drives another 70 km in 1.5 hours. Draw a distance-time graph to illustrate the journey.

Mathematics

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here are the solutions for ITEM 4 and ITEM 5.

ITEM 4
On a journey, Ambrose drives at 50 kmh−150 \text{ kmh}^{-1} for 2 hours, rests for 1 hour and then drives another 70 km70 \text{ km} in 1121\frac{1}{2} hours. Draw a distance time graph to illustrate the journey.

To draw a distance-time graph, we need to determine the total distance covered and the total time taken at different stages of the journey.

  1. Calculate distance and time for the first segment.

    • Speed = 50 kmh−150 \text{ kmh}^{-1}
    • Time = 2 hours
    • Distance = Speed ×\times Time = 50 kmh−1×2 h=100 km50 \text{ kmh}^{-1} \times 2 \text{ h} = 100 \text{ km} At the end of this segment: Time = 2 hours, Distance = 100 km. Point 1: (0,0)(0, 0) Point 2: (2,100)(2, 100)
  2. Calculate distance and time for the resting segment.

    • Time = 1 hour
    • Distance covered = 0 km (during rest, distance remains constant) At the end of this segment: Total Time = 2 h+1 h=3 h2 \text{ h} + 1 \text{ h} = 3 \text{ h}, Total Distance = 100 km. Point 3: (3,100)(3, 100)
  3. Calculate distance and time for the third segment.

    • Distance = 70 km70 \text{ km}
    • Time = 112 h=1.5 h1\frac{1}{2} \text{ h} = 1.5 \text{ h} At the end of this segment: Total Time = 3 h+1.5 h=4.5 h3 \text{ h} + 1.5 \text{ h} = 4.5 \text{ h}, Total Distance = 100 km+70 km=170 km100 \text{ km} + 70 \text{ km} = 170 \text{ km}. Point 4: (4.5,170)(4.5, 170)
  4. Describe the distance-time graph.

    The graph will have "Time (hours)" on the x-axis and "Distance (km)" on the y-axis.

    • From (0,0)(0, 0) to (2,100)(2, 100): A straight line with a positive slope, representing constant speed.
    • From (2,100)(2, 100) to (3,100)(3, 100): A horizontal line, representing no change in distance (rest period).
    • From (3,100)(3, 100) to (4.5,170)(4.5, 170): A straight line with a positive slope, representing constant speed.

    The key points for the graph are:

    • Start: (0 h,0 km)(0 \text{ h}, 0 \text{ km})
    • After 2 hours: (2 h,100 km)(2 \text{ h}, 100 \text{ km})
    • After 3 hours (including 1 hour rest): (3 h,100 km)(3 \text{ h}, 100 \text{ km})
    • After 4.5 hours (total journey): (4.5 h,170 km)(4.5 \text{ h}, 170 \text{ km})

    ITEM 5
    In a survey carried out in a vehicle park, it was found that 40% were saloon cars, 25% buses, 20% lorries and 15% motorcycles. Represent this information on a pie-chart.

    To represent this information on a pie chart, we need to calculate the angle for each category. A full circle is 360∘360^\circ.

  5. Calculate the angle for saloon cars.

    Angle for Saloon Cars=40100×360∘=0.40×360∘=144∘\text{Angle for Saloon Cars} = \frac{40}{100} \times 360^\circ = 0.40 \times 360^\circ = \boxed{144^\circ}
  6. Calculate the angle for buses.

    Angle for Buses=25100×360∘=0.25×360∘=90∘\text{Angle for Buses} = \frac{25}{100} \times 360^\circ = 0.25 \times 360^\circ = \boxed{90^\circ}
  7. Calculate the angle for lorries.

    Angle for Lorries=20100×360∘=0.20×360∘=72∘\text{Angle for Lorries} = \frac{20}{100} \times 360^\circ = 0.20 \times 360^\circ = \boxed{72^\circ}
  8. Calculate the angle for motorcycles.

    Angle for Motorcycles=15100×360∘=0.15×360∘=54∘\text{Angle for Motorcycles} = \frac{15}{100} \times 360^\circ = 0.15 \times 360^\circ = \boxed{54^\circ}
  9. Verify that the sum of the angles is 360∘360^\circ.

    144∘+90∘+72∘+54∘=360∘144^\circ + 90^\circ + 72^\circ + 54^\circ = 360^\circ

    The angles are correct. To draw the pie chart, you would divide a circle into sectors with these calculated angles.

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