© Nuffield Foundation 2011 Free-Standing Mathematics Activity Speed and distance
Speed and distance
Feb 09, 2016
Free-Standing Mathematics Activity. Speed and distance. How can we model the speed of a car? How will the model show the distance the car travels?. v mph. 70. 0. 2. t hours. Using a graph. Think about How far will it travel in 2 hours?. Car travelling at 70 mph. Area = 2 × 70 = 140. - PowerPoint PPT Presentation
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© Nuffield Foundation 2011
Free-Standing Mathematics Activity
Speed and distance
© Nuffield Foundation 2011
• How can we model the speed of a car?• How will the model show the distance the car travels?
© Nuffield Foundation 2011
Using a graph
Car travelling at 70 mph
Area = 2 × 70 = 140
This is the distance travelled, 140 miles
v mph
t hours0 2
70
Think aboutHow far will it travel in 2 hours?
© Nuffield Foundation 2011
Car accelerating steadily from 0 to 72 kph in 10 seconds
Distance travelled = 100 metres
= 100
v kph
t seconds0 10
72
72 kph =
7210006060
10202
= 20 metres per second
20 ms-1
Area of triangle
baseheight2
Think aboutWhat was the car’s average speed? What is the connection with the graph?
© Nuffield Foundation 2011
Car accelerating steadily from 18 ms-1 to 30 ms-1 in 5 seconds
Distance travelled = 120 metres
= 24 × 5
Area of a trapezium
Area =
(1830)52
v ms-1
t seconds0
18
30
5
= 120
(a b) h2
a
b
h
Think aboutWhat was the car’s average speed? What is the connection with the graph?
© Nuffield Foundation 2011
Car travelling between 2 sets of traffic lights
Area of A
252
t (s)v (ms-1)
00
25
48
88
105
120
69
0
v ms-1
t seconds1262 4 8 10
A AC C BB
= 70
Area of C
89 22
= 17
Area of B
58 22
= 13
Total area
= 5
Distance travelled = 70 metres
8
5
9
Think about Why are the strips labelled A, B & C? How will this help to find the area?
Think aboutIs this a good estimate? How can it be improved?Is the graph realistic?
© Nuffield Foundation 2011
Area =
Car travelling with speed v = 0.5t3 – 3t2 + 16
t (s)v (ms-1)
0 1 2 43
16 13.5 8 02.5
v
t0
16
421 3
13.5
82.5
1613.5 12
12.52
13.58 1
2
82.5 1
2
= 14.75 + 10.75+ 5.25 + 1.25
Distance travelled = 32 metres
Think aboutWhat did this car do?
Think aboutHow could this estimate be improved?
© Nuffield Foundation 2011
At the end of the activity
• Explain why using triangles and trapezia can only give an estimate of the area under a curve
• When is an estimate smaller than the actual value? When is it larger?
• How can you improve the estimate?• How well do you think the graphs and functions you
have studied model the actual speed of real cars?• In what way would graphs showing actual speeds
differ from those used in this activity?
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