All you need to know about Distance Time graph for Physics High school

1. Describing a journey made by an
object is very boring if you just
use words

2. Graphs are more revealing

3. Plotting Distance against Time
can tell you a lot about a journey
Time always runs horizontally.
The arrow shows the direction of time
The further to the right, the longer time
from the start
Time
Distance

4. Plotting Distance against Time
can tell you a lot about a journey
Distance runs vertically
The higher up the graph we go, the
further we are from the start.
Time
Distance

5. If something is not moving
Time is increasing to the right
But its distance does not change
Time
Distance

6. For example, an object which is
stopped 30m from the starting
point
Distance/m
Time/s
0
10
20
30
40
0 2 4 6 8 10 12 14

7. If it is stopped when we start
timing, at time zero it will be at a
distance of 30m
Distance/m
Time/s
0
10
20
30
40
0 2 4 6 8 10 12 14

8. After 2 seconds it will still be at
30m
Distance/m
Time/s
0
10
20
30
40
0 2 4 6 8 10 12 14

9. After 6 seconds it will still be at
30m
Distance/m
Time/s
0
10
20
30
40
0 2 4 6 8 10 12 14

10. After 14 seconds it will still be at
30m
Distance/m
Time/s
0
10
20
30
40
0 2 4 6 8 10 12 14

11. So the graph of an object which is
stopped is a horizontal line
Distance/m
Time/s
0
10
20
30
40
0 2 4 6 8 10 12 14

12. Consider an object moving with a
steady speed (say 3m/s)
Distance/m
Time/s
0
10
20
30
40
0 2 4 6 8 10 12 14

13. After 1 second it will have moved a
distance of
Distance/m
Time/s
0
10
20
30
40
0 2 4 6 8 10 12 14

14. After 1 second it will have moved a
distance of 3m
Distance/m
Time/s
0
10
20
30
40
0 2 4 6 8 10 12 14

15. After 2 seconds it will have moved
a distance of
Distance/m
Time/s
0
10
20
30
40
0 2 4 6 8 10 12 14

16. After 2 seconds it will have moved
a distance of 6m
Distance/m
Time/s
0
10
20
30
40
0 2 4 6 8 10 12 14

17. After 4 seconds it will have moved
a distance of
Distance/m
Time/s
0
10
20
30
40
0 2 4 6 8 10 12 14

18. After 4 seconds it will have moved
a distance of 12m
Distance/m
Time/s
0
10
20
30
40
0 2 4 6 8 10 12 14

19. After 8 seconds it will have moved
a distance of
Distance/m
Time/s
0
10
20
30
40
0 2 4 6 8 10 12 14

20. After 8 seconds it will have moved
a distance of 24m
Distance/m
Time/s
0
10
20
30
40
0 2 4 6 8 10 12 14

21. After 12 seconds it will have moved
a distance of
Distance/m
Time/s
0
10
20
30
40
0 2 4 6 8 10 12 14

22. After 12 seconds it will have moved
a distance of 36m
Distance/m
Time/s
0
10
20
30
40
0 2 4 6 8 10 12 14

23. So the graph of an object moving at
a constant speed is a diagonal line
Distance/m
Time/s
0
10
20
30
40
0 2 4 6 8 10 12 14

24. Both lines show that each object
moved the same distance
Distance/m
Time/s
0
10
20
30
40
0 2 4 6 8 10 12 14

25. But the steeper red one got there
first, so it must have travelled faster
Distance/m
Time/s
0
10
20
30
40
0 2 4 6 8 10 12 14

26. The steeper the line is, the faster
an object is travelling
Distance/m
Time/s
0
10
20
30
40
0 2 4 6 8 10 12 14

27. An object that is accelerating
Distance/m
Time/s
0
10
20
30
40
0 2 4 6 8 10 12 14

28. An object that is accelerating
Distance/m
Time/s
0
10
20
30
40
0 2 4 6 8 10 12 14

29. The line is curving upwards. This
shows an increase in speed, since
the gradient is getting steeper
Distance/m
Time/s
0
10
20
30
40
0 2 4 6 8 10 12 14

30. Deceleration
Distance/m
Time/s
0
10
20
30
40
0 2 4 6 8 10 12 14

31. Deceleration
Distance/m
Time/s
0
10
20
30
40
0 2 4 6 8 10 12 14

32. Time
Distance
SUMMARY

33. Time
Distance
SUMMARY
STOPPED

34. Time
Distance
SUMMARY
STOPPED
Distance
Time

35. Time
Distance
SUMMARY
STOPPED
Distance
Time
CONSTANT SPEED

36. Time
Distance
SUMMARY
STOPPED
Distance
Time
CONSTANT SPEED
Distance
Time

37. Time
Distance
SUMMARY
STOPPED
Distance
Time
CONSTANT SPEED
Distance
Time
ACCELERATING

38. What’s happening here?
Distance/m
Time/s
0
10
20
30
40
0 2 4 6 8 10 12 14

39. An object which is stopped 30m
from the start of it’s journey
Distance/m
Time/s
0
10
20
30
40
0 2 4 6 8 10 12 14

40. A reminder
Average speed = distance travelled
time taken
S t
d
x

41. Distance against time graphs
distance
time

42. Let’s go on the corridor!
Quietly and sensibly!
You’ll need a pencil
and your books

43. Distance/time graph
Distance
/m
0 2 4 6 8 10 12 14 16
Time
(slow)/s
0 2.6 4.5 6.9 9.2 10.8 12.7 14.7 16.3
Time
(fast)/s
0 0.9 2.3 3.4 4.4 5.1 6.4 7.3 8.7
Distance/m 18 20 22 24 26 28 30 32
Time (slow/s 18.1 20.2 21.9 23.6 25.8
Time (fast)/s 9.4 11.1 11.9 12.3 14.3

44. No movement?
distance
time

45. No movement
distance
time

46. Constant speed?
distance
time

47. Constant speed
distance
time

48. Constant speed
distance
time
The gradient of this
graph gives the speed

49. Constant speed
distance
time
Δy
Δx
Gradient = Δy/Δx

50. Constant speed
distance
time
How would the
graph look
different for a
faster constant
speed (walking to
Physics)?

51. Constant speed
distance
time
fast

52. Constant speed
distance
time
fast
How would the
graph look
different for a
slower constant
speed (walking to
French)?

53. Constant speed
distance
time
fast
slow

54. Constant speed
distance
time
fast
slow
The gradient of
the graph gives
the speed

55. Let’s go on the corridor!
Quietly and sensibly!
You’ll need a pencil
and your books

56. Distance/time graph -
acceleration
Distance
/m
0 2 4 6 8 10 12 14 16 18
Time/s 0 4.0 6.3 7.4 8.7 9.5 10.1 11.2 11.8 12.0
Distance/m 20 22 24 26 28 30 32
Time/s 12.3 12.6 13.2 13.7

57. Getting faster? (accelerating)
distance
time

58. Getting faster (accelerating)
distance
time

59. Examples
distance
time

60. A car accelerating from stop and
then hitting a wall
distance
time

61. A car accelerating from stop and
then hitting a wall
distance
time

62. Speed against time graphs
speed
time

63. Speed against time graphs
speed
time

64. No movement?
speed
time

65. No movement
speed
time

66. Constant speed?
speed
time

67. Constant speed
speed
time

68. Constant speed
speed
time
How would the
graph look
different for a
faster constant
speed?

69. Constant speed
speed
time
fast

70. Constant speed
speed
time
fast
How would the
graph look
different for a
slower constant
speed?

71. Constant speed
speed
time
fast
slow

72. Getting faster? (accelerating)
speed
time

73. Getting faster? (accelerating)
speed
time
Constant acceleration

74. Getting faster? (accelerating)
speed
time
The gradient of this
graph gives the
acceleration

75. Acceleration
speed
time
a = v – u
t
(v= final speed, u = initial speed)
v
u

76. Acceleration (m/s2)
acceleration = change in speed
time taken
a = v – u
t
a = acceleration (m/s2)
v = final speed (m/s)
u = initial speed (m/s)
t = time taken (s)
Can you copy this please?

77. Getting faster? (accelerating)
speed
time
The area under the graph
gives the distance travelled

78. Example:
speed
time

79. A dog falling from a tall building
(no air resistance)
speed
time

80. A dog falling from a tall building
(no air resistance)
speed
time

81. A dog falling from a tall building
(no air resistance)
speed
time
Area = height of building

82. Be careful!
distance
time
speed
time

83. No movement
distance
time
speed
time

84. Constant speed
distance
time
speed
time
Area under graph =
distance travelled
gradient = speed

85. Constant acceleration
distance
time
speed
time
Area under graph =
distance travelled
Gradient =
acceleration =
a = (v-u)/t

86. • Presentation by Keith Jarvis and
SharemyLesson Science Team
• Distributed by Stoplearn.com