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Distance, time and speed. To work out the speed of an object you need to know:. the distance travelled. how long it took to travel that distance. Calculating average speed. Average speed is calculated using this equation:. d. total distance. Average speed. =. total time. s. t. - PowerPoint PPT Presentation
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3 of 24 © Boardworks Ltd 2008
To work out the speed of an object you need to know:
Distance, time and speed
the distance travelled how long it took to travel that distance.
4 of 24 © Boardworks Ltd 2008
Average speed is calculated using this equation:
Speed can be measured in different units, e.g. m/s, km/h, km/s, miles per hour.
The units of distance and time will determine the units to be used for speed.
Calculating average speed
d
s t
formula triangle
total distance
total time
Averagespeed
=
7 of 24 © Boardworks Ltd 2008
A girl takes 30 minutes to travel around a cross-country ski course: a distance of 10 km. Calculate her average speed in km/h.
20 km/h
Speed calculation example
distance (in km)average speed (in km/h) time (in h)
=
10 km
0.5 h=
10 km=
8 of 24 © Boardworks Ltd 2008
Sometimes the units have to be changed in a speed calculation.
Speed calculation example – units
Calculate the average speed of the skier in m/s.
10 km
2.8 m/s
average speed (in m/s) time (in s)
=distance (in m)
3600 s10,000 m
= =
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= 3.6 km/h × 0.5 h
distance (km) = speed (km/h) × time (h)
A boy sets off for a walk around his village at an average speed of 3.6 km/h. How far will he travel in 30 minutes?
Give your answer in km.
Distance calculation
= 1.8 km
10 of 24 © Boardworks Ltd 2008
How long would it take the boy to walk 200 m to the church, if his average speed was 0.8 m/s?
Time calculation – question 1
time =distance
speed
= 250 seconds
200 m
0.8 m/s =
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The gradient of the line in adistance–time graph equals the speed.
Calculating speed from the gradient
The slope of a graph is called the gradient.
It is difficult to calculate the gradient of ‘realistic’ graphs because the line is curved.
Simple graphs use straight lines only, making it easy to calculate the gradient.
time
dis
tan
ce
time
dis
tan
ce
15 of 24 © Boardworks Ltd 2008
What is the speed of the object between points A and B?
time (s)
dis
tan
ce (
m)
0 21 3 4 5 6 7 8 90
10
20
30
40
50
60
70
A
B the object has moved
60 m (70 – 10 )
it took 3 s to move this distance (6 – 3)
speed = distance/time
= 60/3
= 20 m/s
What’s the speed?
18 of 24 © Boardworks Ltd 2008
How can we work out the average speed of this object between points C and D?
time (s)
dis
tan
ce (
m)
0 21 3 4 5 6 7 8 90
10
20
30
40
50
60
70
A
B the object has moved
70 m (70 – 0 )
it took 9 s to move this distance (9 – 0)
speed = distance/time
= 70/9
= 7.8 m/s
What’s the speed?
C
D
19 of 24 © Boardworks Ltd 2008
The speed of a race car at any point around a track is called the instantaneous speed. A car will have a different instantaneous speed at each of the points around the track.
Average speed is the total distance travelled divided by the total time taken. It is never bigger than the instantaneous speed.
Average speed vs. instantaneous speed