1. B Motion graphs Motion graphs Distance-time graphs
Curves on distance-time graphs
Example: Calculations on distance-time graphs
Using a ticker-timer to make a record of a journey
Speed-time graphs
Example: Acceleration from a speed-time graph
Example: Distance from a speed-time graph

2. Motion graphs
Motion graphs are graphs that describe a motion in graphical form.
You will need to interpret distance–time and speed– time graphs for this standard.
distance
(m)
time (s)

3. Do this experiment from your Workbook.
1B 1 Graphing a journey

4. Distance–time graphs
distance
(m)
time (s)
The gradient of the line shows the speed over that straight part of the graph.
where
and

5. Faster speed Steeper gradient Slow speed Shallow gradient distance (m)
time (s)

6. Slope of distance–time graph gives speed
The steeper the gradient (slope) of the line, the higher the speed.
If the line is horizontal the speed is zero, the object is stopped.
Average speed = the total distance ÷ total time
distance
(m)
Zero speed, stopped
Faster constant speed
Slow constant speed
time (s)

7. Shaun stationary - stopped2 4 6 8 10 12 14 20 40 60 80
100
distance
(m)
time (s)

8. Shaun at constant speed2 4 6 8 10 12 14 20 40 60 80
100
distance
(m)
time (s)
How far has he gone after 10 s?
80 m

9. Shaun at different constant speeds2 4 6 8 10 12 14 20 40 60 80
100
distance
(m)
time (s)
Fast constant speed
Slow constant speed

10. Distance-time graphs
Distance
(m)
time (s)
Gradient of a section shows the speed:
The steeper the gradient the higher the speed.
A horizontal line means the object is stationary; it has zero speed.

11. Curves on distance-time graphs
If the line curves, the object is getting faster or slower. 2 4 6 8 10 12 14 20 40 60 80
100
distance
(m)
time (s)
Slowing down
Speeding up

12. Shaun accelerating distance (m) time (s) 2 4 6 8 10 12 14 20 40 60 802 4 6 8 10 12 14 20 40 60 80
100
distance
(m)
time (s)

13. Shaun decelerating distance (m) time (s) 2 4 6 8 10 12 14 20 40 60 802 4 6 8 10 12 14 20 40 60 80
100
distance
(m)
time (s)

14. Curves on distance-time graphs
A curve on a distance-time graph means that the speed is changing, ie the object is accelerating.
If the curve turns up, the object is speeding up.
If the curve turns down, the object is slowing down. d d t t
acceleration
deceleration

15. Example: Calculations on distance-time graphs
d1 = , d2 = ,
t1 = , t2 = ,
v =
2 m
8 m 10
5 s
20 s 8 ? 6 4 2 5 10 15 20 25
time (s)
Find the speed of the object between five and twenty seconds.

16. Example: Calculations using distance-time graphs graphs
Example: Calculations on distance-time graphs
Distance
(m)
d1 = 2 m, d2 = 8 m,
t1 = 5 s, t2 = 20 s,
v = ? 10 8 6 4 2 5 10 15 20 25
time (s)
Find the speed of the object between five and twenty seconds.
1B 2 Time trials 1B 3 A walk to the Post Shop

17. Using a ticker-timer to make a record of a journey
Cut a length of ticker-tape about 2 m long.

18. hammer
Thread it through the ticker-timer, so that it goes underneath the hammer and through both guides.
If you need carbon paper, put it between the hammer and the tape.

19. Connect the ticker-timer to the AC terminals of a power supply.

20. As the Alternating Current turns on and off 50 times per second, it makes the hammer hit the tape 50 times per second.
This tape contains ink so that each time it is hit a dot is made.
When the tape moves, the dots provide a record of the journey.

21. Stick the end of the tape to the back of a trolley with a small piece of sellotape and bring the trolley close to the ticker-timer.

22. Switch the power supply on and give the trolley a gentle push.

23. As the trolley moves, it pulls the tape through the ticker-timer.
The trolley moves quickly at first, but rapidly slows to a stop.
The dots on the tape form a record of this journey.

24. Draw a line through every 5th dot. This divides the tape into 0
Draw a line through every 5th dot. This divides the tape into 0.1 s intervals.

25. The 0.1 s segments change length as the trolley slows down.

26. Cut the tape along each line...

27. ... and position them, in order, along a line to make a graph of the journey.

28. You can make the record permanent by holding the strips together with sellotape.

29. Each strip shows the distance travelled by the trolley over the 0
Each strip shows the distance travelled by the trolley over the 0.1 s interval.
We have made a speed-time graph of the trolley’s journey as it slowed down.
1B 4 Testing ticker-timers 1B 5 Going dotty

30. Speed-time graphs
speed
(m s-1)
time (s)
The gradient of the line shows the acceleration over that straight part of the graph.
where
and

31. Slope of speed–time graph gives acceleration
The steeper the gradient (slope) of the line, the higher the acceleration.
If the line is horizontal, the speed is constant; zero acceleration.
If the gradient is negative, the acceleration is negative; deceleration.
Speed
(m s-1)
Constant speed, zero acceleration
Negative acceleration,
deceleration
Higher constant acceleration
Constant acceleration
time (s)

32. The area under a speed-time graph shows the distance travelled.
(m s-1)
Area = distance travelled
time (s)

33. Speed-time graphs A speed-time graph shows how the speed changes.
Gradient of a section is equal to
Speed
(m s-1)
time (s)
the acceleration in that time period.
The steeper the gradient, the higher the acceleration.
If the line is horizontal, the object is moving at a constant speed and the acceleration is zero.
A negative gradient (sloping down) shows a negative acceleration, (deceleration).
The area under the graph gives the distance travelled.

34. Example: Acceleration from a speed-time graph v1 = v2 = t1 = t2 = a =
10 m s-1
40 m s-1
Speed
(m s-1) 50
5 s
20 s 40 ? 30 20 10 5 10 15 20 25
time (s)
Find the acceleration of the object between five and twenty seconds.

35. Example: Acceleration from a speed-time graph
(m s-1)
v1 = 10 m s-1, v2 = 40 m s-1,
t1 = 5 s, t2 = 20 s,
v = ?
10 m s-1
40 m s-1 50
5 s
20 s 40 ? 30 20 10 5 10 15 20 25
time (s)
Find the acceleration of the object between five and twenty seconds.

36. Example: Distance from a speed-time graph
Find the distance travelled by the object between five and twenty seconds.
[Hint: the area under a speed-time graph is the distance.]
Speed
(m s-1) 50 40 30 20 10 5 10 15 20 25
From the previous calculation:
Initial velocity v1 = 10 m s-1, Δv = 30 m s-1,
Δ t = 15 s, distance = ?
time (s)

37. Example: Distance from a speed-time graph
Find the distance travelled by the object between five and twenty seconds.
[Hint: the area under a speed-time graph is the distance.]
Speed
(m s-1) 50 40 30 20 10
From the previous calculation:
Initial velocity v1 = 10 m s-1, Δv = 30 m s-1,
Δ t = 15 s, distance = ? 5 10 15 20 25
time (s)
10 m s-1
30 m s-1
15 s ?
1B 6 Speed-time graphs

38. Proceed to next chapter
End of chapter
Proceed to next chapter