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.)