Post on 30-Dec-2015
SPEED, DISTANCE AND TIME
Changing units of time
1 Write 24 minutes as a fraction of an hour.
24 minutes =
24
60 hour
2
5 hour
to change minutes into hours divide by 60
2 Write 54 minutes as a decimal of an hour.
54 minutes =
54
60 hour
9
10 hour
to change minutes into hours divide by 60to change a fraction to a decimal divide the numerator by the denominator 0.9 hours
7
1260 minutes
35 minutes
to change hours into minutes multiply by 60
3 Change of an hour into minutes.
7
12
7
12 hour =
0.3 60 minutes
18 minutes
to change hours into minutes multiply by 60
4 Change 0.3 hours into minutes.
0.3 hour =
Speed
Speed is a measure of how fast an object is travelling.
When the speed is constant, the formula connecting speed, distance and time is:
speed =
distance
time
If the distance is measured in metres and the time is measured in seconds then the speed is measured in metres per second (m/s or ms−1).
If the distance is measured in kilometres and the time is measured in hours then the speed is measured in kilometres per hour (km/h or kmh−1).
1 A car takes 3 hours 20 minutes to travel 300 km at constant speed.
Find the speed of the car in km/h.
speed =
distance
time
300
313
90 km/h
You must first change 20 minutes into hours.
20 minutes =
20
60 hour =
1
3 hour
2 A car is travelling at 54 km/h. Change the speed of the car into m/s.
54 kilometres/hour = 54 000 metres/hour
54 000
metres/minute60
900 metres/minute
900
60 metres/second
15 m/s
The formula can be rearranged to give speed =
distance
time
distance = speed × time time =
distance
speedor
D
S × T
The following triangle is a useful memory aid for remembering the three formulae.
To find the formula for finding T put your finger over the letter T.
This gives you T =
D
S.
To find the formula for finding D put your finger over the letter D.
This gives you D = S T.
A bird flies for 48 km at a speed of 6 m/s.Calculate the time taken in hours and minutes.
48 km = 48 000 m
time =
distance
speed
48 000
6
8000 seconds
133
1
3 minutes
2 hours 13
1
3 minutes
change 48 km into m
divide by 60 to change into minutes120 minutes = 2 hours
Average speed
You can calculate the average speed for a journey using:
average speed =
total distance travelled
total time taken
A car travels at 75 km/h for 3 hours and then at 60 km/h for 30 minutes.a Calculate the total distance travelled.b Calculate the average speed for the whole journey.
a distance = speed × time
distance = 75 3 225 km
distance = 60 0.5 30 km
Total distance = 225 + 30 = 255 km
b average speed =
total distance travelled
total time taken
255
3 0.5
72.9 km/h (to 3 s.f.)