The document discusses travel graphs and displacement-time graphs. It provides an example graph of a ball being bounced and its height over time. It then works through several examples calculating values from the graph, including: 1) The height of the ball after 1 second is 35 meters. 2) The ball will be at the same height of 35 meters again at 7 seconds. 3) The average velocity during the first second is 35 m/s. 4) The average velocity during the fifth second is -5 m/s. 5) The average speed during the 8 seconds the ball was in the air was 20 m/s.

1. Travel Graphs

2. Travel Graphs
e.g. A ball is bounced and its distance from the ground is graphed.
x
80 x  5t  8  t 
60
40
20
2 4 6 8 t

3. Travel Graphs
e.g. A ball is bounced and its distance from the ground is graphed.
x
80 x  5t  8  t 
60
40
20
2 4 6 8 t
Distance = total amount travelled

4. Travel Graphs
e.g. A ball is bounced and its distance from the ground is graphed.
x
80 x  5t  8  t 
60
40
20
2 4 6 8 t
Distance = total amount travelled
Displacement = how far from the starting point

5. Travel Graphs
e.g. A ball is bounced and its distance from the ground is graphed.
x
80 x  5t  8  t 
60
40
20
2 4 6 8 t
Distance = total amount travelled
Displacement = how far from the starting point
(i) Find the height of the ball after 1 second

6. Travel Graphs
e.g. A ball is bounced and its distance from the ground is graphed.
x
80 x  5t  8  t 
60
40
20
2 4 6 8 t
Distance = total amount travelled
Displacement = how far from the starting point
(i) Find the height of the ball after 1 second
when t  1, x  5 1 8  1
 35

7. Travel Graphs
e.g. A ball is bounced and its distance from the ground is graphed.
x
80 x  5t  8  t 
60
40
20
2 4 6 8 t
Distance = total amount travelled
Displacement = how far from the starting point
(i) Find the height of the ball after 1 second
when t  1, x  5 1 8  1
 35
After 1 second the ball is 35 metres above the ground

8. (ii) At what other time is the ball this same height above the ground?

9. (ii) At what other time is the ball this same height above the ground?
when x  35,

10. (ii) At what other time is the ball this same height above the ground?
when x  35, 5t  8  t   35
t 8  t   7
8t  t 2  7
t 2  8t  7  0
 t  1 t  7   0
t  1 or t 7

11. (ii) At what other time is the ball this same height above the ground?
when x  35, 5t  8  t   35
t 8  t   7
8t  t 2  7
t 2  8t  7  0
 t  1 t  7   0
t  1 or t  7
 ball is 35 metres above ground again after 7 seconds

12. (ii) At what other time is the ball this same height above the ground?
when x  35, 5t  8  t   35
t 8  t   7
8t  t 2  7
t 2  8t  7  0
 t  1 t  7   0
t  1 or t  7
 ball is 35 metres above ground again after 7 seconds
change in displacement
Average velocity =
change in time

13. (ii) At what other time is the ball this same height above the ground?
when x  35, 5t  8  t   35
t 8  t   7
8t  t 2  7
t 2  8t  7  0
 t  1 t  7   0
t  1 or t  7
 ball is 35 metres above ground again after 7 seconds
change in displacement
Average velocity =
change in time
x2  x1

t2  t1

14. (iii) Find the average velocity during the 1st second

15. (iii) Find the average velocity during the 1st second
x2  x1
average velocity 
t2  t1
35  0

1 0
 35

16. (iii) Find the average velocity during the 1st second
x2  x1
average velocity 
t2  t1
35  0

1 0
 35
 average velocity during the 1st second was 35m/s

17. (iii) Find the average velocity during the 1st second
x2  x1
average velocity 
t2  t1
35  0

1 0
 35
 average velocity during the 1st second was 35m/s
(iv) Find the average velocity during the fifth second

18. (iii) Find the average velocity during the 1st second
x2  x1
average velocity 
t2  t1
35  0

1 0
 35
 average velocity during the 1st second was 35m/s
(iv) Find the average velocity during the fifth second
when t  4, x  5  4  8  4 
=80

19. (iii) Find the average velocity during the 1st second
x2  x1
average velocity 
t2  t1
35  0

1 0
 35
 average velocity during the 1st second was 35m/s
(iv) Find the average velocity during the fifth second
when t  4, x  5  4  8  4 
=80
when t  5, x  5  5  8  5 
=75

20. (iii) Find the average velocity during the 1st second
x2  x1
average velocity 
t2  t1
35  0

1 0
 35
 average velocity during the 1st second was 35m/s
(iv) Find the average velocity during the fifth second
x2  x1
when t  4, x  5  4  8  4  average velocity 
t2  t1
=80
75  80
when t  5, x  5  5  8  5  
54
=75  5

21. (iii) Find the average velocity during the 1st second
x2  x1
average velocity 
t2  t1
35  0

1 0
 35
 average velocity during the 1st second was 35m/s
(iv) Find the average velocity during the fifth second
x2  x1
when t  4, x  5  4  8  4  average velocity 
t2  t1
=80
75  80
when t  5, x  5  5  8  5  
54
=75  5
 average velocity during the 5th second was  5m/s

22. (iv) Find the average velocity during its 8 seconds in the air

23. (iv) Find the average velocity during its 8 seconds in the air
x2  x1
average velocity 
t2  t1
00

80
0

24. (iv) Find the average velocity during its 8 seconds in the air
x2  x1
average velocity 
t2  t1
00

80
0
 average velocity during the 8 seconds was 0m/s

25. (iv) Find the average velocity during its 8 seconds in the air
x2  x1
average velocity 
t2  t1
00

80
0
 average velocity during the 8 seconds was 0m/s
distance travelled
Average speed =
time taken

26. (iv) Find the average velocity during its 8 seconds in the air
x2  x1
average velocity 
t2  t1
00

80
0
 average velocity during the 8 seconds was 0m/s
distance travelled
Average speed =
time taken
(v) Find the average speed during its 8 seconds in the air

27. (iv) Find the average velocity during its 8 seconds in the air
x2  x1
average velocity 
t2  t1
00

80
0
 average velocity during the 8 seconds was 0m/s
distance travelled
Average speed =
time taken
(v) Find the average speed during its 8 seconds in the air
distance travelled
average speed 
time taken

28. (iv) Find the average velocity during its 8 seconds in the air
x2  x1
average velocity 
t2  t1
00

80
0
 average velocity during the 8 seconds was 0m/s
distance travelled
Average speed =
time taken
(v) Find the average speed during its 8 seconds in the air
distance travelled
average speed 
time taken
160

8
 20

29. (iv) Find the average velocity during its 8 seconds in the air
x2  x1
average velocity 
t2  t1
00

80
0
 average velocity during the 8 seconds was 0m/s
distance travelled
Average speed =
time taken
(v) Find the average speed during its 8 seconds in the air
distance travelled
average speed 
time taken
160

8
 20
 average speed during the 8 seconds was 20m/s

30. Exercise 3A; 2, 4, 6, 7, 8, 10, 11, 13