A car travels at an average speed of 74.5 km/h for 2.25 hours.

  1. (a)

    Convert 75 km/h to m/s.

    Answer ... m/s

  2. (b)

    By rounding the numbers correct to 1 significant figure, find an estimate of the distance travelled by the car. Show your working clearly.

    Answer ... km

  3. (c)

    Without doing any calculation, explain why the actual distance travelled by the car is greater than the answer to (b).

    Answer

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Worked solution

7(a)

1. Use the conversion factors for kilometres and hours.

75 km/h=75×1000 m3600 s75\text{ km/h}=75\times \dfrac{1000\text{ m}}{3600\text{ s}}

2. Calculate the speed in metres per second.

75×10003600=20.833…75\times \dfrac{1000}{3600}=20.833\ldots

Answer

20.8 m/s20.8\text{ m/s}

7(b)

1. Round the speed and time to 1 significant figure.

74.5 km/h≈70 km/h74.5\text{ km/h} \approx 70\text{ km/h}

2.25 h≈2 h2.25\text{ h} \approx 2\text{ h}

2. Estimate the distance using distance equals speed multiplied by time.

Estimated distance
=70×2=140 km= 70 \times 2 = 140\text{ km}

Answer

140 km140\text{ km}

7(c)

1. Explain how the rounding affected the estimate.

In part (b), 74.5 km/h74.5\text{ km/h} was rounded down to 70 km/h70\text{ km/h} and 2.25 h2.25\text{ h} was rounded down to 2 h2\text{ h}. Since distance == speed ×\times time, using smaller values gives a smaller distance than the actual distance.

Answer

The speed 74.5 km/h74.5\text{ km/h} was rounded down to 70 km/h70\text{ km/h} and the time 2.25 h2.25\text{ h} was rounded down to 2 h2\text{ h}, so the estimated distance is less than the actual distance.

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