math(f5) gradient and area under a graph
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GRADIENT AND AREA UNDER A GRAPH
Distance-Time Graph How to draw a graph? Recall previous knowledge
• x axis represent time• y axis represent distance
Note : When a distance-time graph is drawn, the
gradient of the graph gives the speed.
Example
The following table shows the distance travelled and time taken by Amin to his office. Draw the distance-time graph made by Amin
Time (hours)
0.1 0.2 0.3
Distance (km)
5 10 15
The Gradient of a Distance-Time GraphWhat is gradient?
- Is the change of the quantity on the vertical axis with respect to the change of the quantity on the horizontal axis
How to find gradient? Recall the formula of gradient :
m =
Example :…………..
What is the general equation of straight line?
The gradient of distance-time graph represent speed
12
12
xx
yy
Please do worksheet 1…Exercise 6.1 B and
6.1 C with your partner
Exercise
How to find speed for a period of time from a distance-time graph
Notes:
Time
DistanceSpeed
Taken Time Total
Travelled Distance TotalSpeed Average
The distance-time graph shows the distance covered by a boy from the starting point to another point and back.
Example:
a) Find the speed for the first 15 seconds.
b) How long did he rest?
c) Find the speed where the boy back to starting point.
d) Find the average speed for the whole journey.
From the graph,
a)Find the speed for the first 15 seconds.Answers:a) Speed for the first 15 seconds:
sm
s
m
/3
20
0-15
0-100
Time
DistanceSpeed
Answers:b) How long did he rest?
Time taken = 30s – 15s = 15 seconds
-He takes 15 seconds to rest
Answers:c) The speed where the boy back to the starting
point:
sms
ms
m
/ 5 20
100
30-50
100-0
Time
DistanceSpeed
Negative sign indicates the
direction of the journey is reversed
Answers:d)
sms
m
/ 2 50
100
Taken Time Total
Travelled Distance TotalSpeed Average
Please do worksheet 1. Exercise 6.1 D
Exercise
Answers for Worksheet 1 (6.1D) a) Speed from technician workshop to the
house of the first customer:
154
6010
9
Time
DistanceSpeed
kmh
hours
km
b) Speed from 1st customer house to the 2nd customer house (BC):
124
603040
95
Time
DistanceSpeed
kmh
hours
kmkm
c)
143.15
6070
81
Taken Time Total
Travelled Distance TotalSpeed Average
kmh
hours
km
Please do worksheet 2
Exercise
Submit it after the end of the class
SUMMARY Gradient of a graph is the rate of change
in the quantity on the vertical axis with respect to the change in the quantity on the horizontal axis.
Gradient of the distance-time graph represents the speed.
Formula used:
12
12mxx
yy
Taken Time Total
Travelled Distance TotalSpeed Average
Time
DistanceSpeed
homework (ex6.1(d) , no 3&4)