1.4 Converting
Graphs
Types of Motion:
Displacement & Velocity
Graphs
Slope of displacement-time graph give
velocity
Area of velocity-time graph gives the
displacement
Displacement & Velocity
Graphs
Slope of velocity-time graph give
acceleration
Area of acceleration-time graph gives the
velocity
[S]
1.4 Comparing Graphs
→
v-t Graph:
Converting Graphs
[S]
Example #7:
Use the graph above to
answer the following
questions.
a) What is the velocity at t =3.0 s?
Answer
At 3.0 s, the velocity is 6 m/s [S]
→
V-T Graphs
v-t Graph:
[S]
Example #7:
b) What is the average
velocity from 0s to 10s?
𝑡𝑜𝑡𝑎𝑙 𝑑𝑖𝑠𝑝𝑙𝑎𝑐𝑒𝑚𝑒𝑡
𝑎𝑣𝑒𝑟𝑎𝑔𝑒 𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦 =
𝑡𝑜𝑡𝑎𝑙 𝑡𝑖𝑚𝑒
1
1
𝑇𝑜𝑡𝑎𝑙 𝑑𝑖𝑠𝑝𝑙𝑎𝑐𝑒𝑚𝑒𝑛𝑡 = 𝑏ℎ + 𝐿𝑊 = 𝑥4𝑠 𝑥 8 𝑚/𝑠[𝑆] + 6𝑠𝑥8𝑚/𝑠[𝑆]
2
2
𝑡𝑜𝑡𝑎𝑙 𝑑𝑖𝑠𝑝𝑙𝑎𝑐𝑒𝑚𝑒𝑛𝑡 = 16𝑚 𝑆 + 48 𝑚 𝑆 = 64 𝑚[𝑆]
𝑎𝑣𝑒𝑟𝑎𝑔𝑒 𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦 =
64 𝑚[𝑆]
𝑚
= 6.4 [𝑆}
10 𝑠
𝑠
Average velocity is 6.4 m/s [S]
Converting Graphs
[S]
Example #7:
c) Make a position-time from
0s to 10s.
Obtain the displacements
by calculating the area.
Determine the position by
adding areas
→
v-t Graph:
Converting Graphs
v-t Graph:
Time
(s)
Displacement(area) [S]
Position m[S]
Sum
displscement
0
0
0
1
Displacement between 0 to
1s = 0.5 x 1sx1m/s =1 m
1
2
0.5 x(2m/s +4m/s)1s =3m
1+3 = 4
3
0.5 x (4m/s + 6m/s)1s =5m
9 =4 + 5
4
0.5 x (6m/s + 8 m/s) 1s =7 m
16
5
Displacement from 4s to 5s
=1s x 8m/s= 8m
24
6
1 s x 8 m/s =8 m
32
7
1 s x 8 m/s =8 m
40
8
1 s x 8 m/s =8 m
48
9
1 s x 8 m/s =8 m
56
10
1 s x 8 m/s =8 m
64
[S]
The area for the displacement between 1s to 2s is a trapezoid.
The area is easily calculated using ½(sum of parallel sides)x
Comparing Graphs
Example #7 Soln:
c)
Time (in s)
Position (in m [E])
0
0
1
1
2
4
3
9
4
16
5
24
6
32
7
40
8
48
9
56
10
64
1.4 Comparing Graphs
Example #7 Soln:
0
0
1
1
2
4
3
9
4
16
5
24
6
32
7
40
8
48
9
56
10
64
70
60
50
Position (m [S])
c)
Time Position
(in s) (in m
[S])
Position-time graph
40
30
20
10
0
0
2
4
6
8
10
time (s)
The position-time graph curves smoothly
upwards from 0 s to 4s as the objects
accelerates uniformly from 0 to 8m/s.
From 4 s to 10 s the graph is a straight line
sloping upwards as the object travels with
uniform velocity of 8 m/s [S].
12
1.4 Comparing Graphs
d)
Calculate the acceleration and draw an
acceleration-time graph
The acceleration is constant from 0s to 4s which is the
slope.
Slope = rise/run
𝑠𝑙𝑜𝑝𝑒 =
𝑟𝑖𝑠𝑒
𝑟𝑢𝑛
𝑚
=
8 𝑠 𝑆 −0
4𝑠−0
From 4s to 10 s 𝑠𝑙𝑜𝑝𝑒 =
= 2.0
𝑚
𝑠2 𝑆
8𝑚
−8𝑚/𝑠[𝑆]
𝑠𝑆
10𝑠 −4𝑠
= 0 m/𝑠 2
1.4 Comparing Graphs
Time acceleration
(in s) m/s2 [S])
2
1
2
2
2
3
2
4
2
4
0
5
0
6
0
7
0
8
0
9
0
10
0
2,5
2
Acceleration(m/s2 [S])
0
Acceleration-time Graph
1,5
1
0,5
0
0
2
4
6
8
10
Time (s)
Note the acceleration instantaneously
change from 2 m/s2 to 0 m/s2 at 4s. This is
shown by having two values at t=4 s.
12
1.4 Comparing Graphs
What is the motion in each section of the following
graph?
→
v-t Graph:
B
[W]
C
A
D
1.4 Comparing Graphs
What is the motion in each section of the following
graph?
→
v-t Graph:
B
[W]
A
C
D
1.4 Comparing Graphs
What is the motion in each section of the following graph?
→
v-t Graph:
A
B
C
D
1.4 Comparing Graphs
1.4 Practice Questions:
Page 34 Practice Q1
Page 35 Practice Q1-4
Finish Graph Worksheet