10. The table shows some of the fl ights leaving Dublin airport for London Heathrow on a particular day.
(i) Stephen must be in London for a business meeting at 12:30 pm. The hotel where the meeting is being held is half an hour from Heathrow airport. What is the latest fl ight he can take from Dublin airport? Justify your answer with mathematical calculations.
(ii) How long will Stephen’s fl ight take?
(iii) Stephen lives 45 minutes from Dublin airport. He would like to be at the airport 1 hour before his fl ight. What time will he have to leave his house to do this?
14·2 Speed
A rate of change is a relationship between two quantities.
Speed is a rate of change, commonly used in everyday life. It is the rate of change of distance in relation to time. Speed is the distance travelled per unit time.
Average speed = distance travelled
____________ time taken
To calculate speed, we need to know the distance travelled and the time taken to travel this distance.
The units used to measure speed are a combination of the unit of distance and the unit of time.
If an object is travelling at 100 km/hr, this means that in 1 hour it would travel an average distance of 100 km, in 2 hours 200 km, and in half an hour 50 km.
We can be given any two of the three measurements: speed, distance or time, and asked to calculate the third measurement, so we need to remember three formulae to do this:
Speed = distance
____________ time
Time = distance
____________ speed
Distance = speed × time To help us remember these formulae we can use the Distance–Speed–Time triangle.
Cover the measurement you are trying to fi nd. For example, if we cover ‘speed’, we are left with distance over time. If we want to fi nd a distance, we cover ‘distance’, we are left with speed × time.
Speed as a ratio A ratio is a way of comparing numbers.
S Speed
Speed can be written as the ratio of distance to time and is written as distance : time. A speed of 80 km/hr can be written as a ratio in the form 80 : 1
D Distance T Time
The most common units of speed are metres per second (m/s) and kilometres per hour (km/hr).
Departing DUB 06:40
DUB 07:30 DUB 08:50 DUB 09:50 DUB 12:10 DUB 13:40 DUB 14:40 DUB 15:50
Arriving
LHR 08:05 LHR 09:05 LHR 10:15 LHR 11:10 LHR 13:25 LHR 14:55 LHR 15:55 LHR 17:10
By the end of this section you should: ● understand that speed is a rate of change
● be able to use the speed formula to calculate speed, distance and time using correct units
● be able to use the ratio method to calculate speed, distance and time using correct units
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Linking Thinking 1
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