1. Graphing with Uncertainties
Experimental data will contain uncertainties
These uncertainties now need to be considered when trying to determine the relationship between variables
Error bars are used to show the uncertainty in individual data points
Lines of best & worst fit are used to find the overall uncertainty in the relationship

2. θ Determine the acceleration… a 0.5 0.3 1 1.15 1.5 1.9 2 4.5 2.5 7.5 3
Time (s)
d(cm)
0.5
0.3 1
1.15
1.5
1.9 2
4.5
2.5
7.5 3
10.2
3.5
14.5 4 19 a θ
What are the Independent , dependent & control variables?
Uncertainty in time values is ±0.05 s and d values are ±10%

3. Raw Data with uncertainty
Time (s)
± (s)
d(cm)
± d(cm)
0.5
0.05
0.3
0.03 1
1.15
0.1
1.5
1.9
0.2 2
4.5
2.5
7.5
0.8 3
10.2
3.5
14.5 4 19
Uncertainty in time values is ±0.05 s and d values are ±10%

4. Raw Data with uncertainty
Time (s)
± (s)
d(cm)
± d(cm)
0.5
0.05
0.3
0.03 1
1.15 or 1.2
0.1
1.5
1.9
0.2 2
4.5
2.5
7.5
0.8 3
10.2 or 10
3.5
14.5 or 15 4 19
Uncertainty in time values is ±0.05 s and d values are ±10%

5. Not linear… guess relationship
d(cm)
Time (s)
Not linear… guess relationship

6. Transform data & uncertainties
t (s) ±%
t2(s2)
d (cm)
0.5
0.05 10
0.25 20
0.3
0.03 1 5
1.0
0.1
1.15
1.2
1.5
3.3
2.3
6.6
1.9
0.2 2
2.5
4.0
4.5
6.3 4
7.5
0.8 3
1.7
9.0
3.4
10.2
3.5
1.4
12.3
2.8
14.5 15
1.3
16.0
2.6
0.4 19
t (s)
d + 10% (cm)

7. Transform data & uncertainties
t (s) ±%
t2(s2)
d (cm)
0.5
0.05 10
0.25 20
0.3
0.03 1 5
1.0
0.1
1.15
1.2
1.5
3.3
2.3
6.6
1.9
0.2 2
2.5
4.0
4.5
6.3 4
7.5
0.8 3
1.7
9.0
3.4
10.2
3.5
1.4
12.3
2.8
14.5 15
1.3
16.0
2.6
0.4 19
t (s)
d + 10% (cm)

9. Transform data & uncertainties
t (s) ±%
t2(s2)
d (cm)
0.5
0.05 10
0.25 20
0.3
0.03 1 5
1.0
0.1
1.15
1.2
1.5
3.3
2.3
6.6
1.9
0.2 2
2.5
4.0
4.5
6.3 4
7.5
0.8 3
1.7
9.0
3.4
10.2
3.5
1.4
12.3
2.8
14.5 15
1.3
16.0
2.6
0.4 19
t (s)
d + 10% (cm)

10. Draw in line of WORST fit This is some what arbitrary!
Add error bars
Draw in line of BEST fit
Draw in line of WORST fit
This is some what arbitrary!

11. Calculate gradients & record intercepts for BOTH lines
Line of best fit
Line of worst fit
Line of Best fit:
Intercept = m
Gradient = 1.21 (3sf)
(from graphing calc)
LABEL the lines
Calculate gradients & record intercepts for BOTH lines
Line of worst fit:
Intercept = 0.5 m
Gradient = (16-2)/(15-2) = 1.08

13. State the relationship between the variables
Line of best fit: Intercept = cm
Gradient = 1.21 cms-2
Line of worst fit: Intercept = 0.5 cm
Gradient = cms-2
Error uncertainties:
Intercept = ( ) = ± 0.8 cm
Gradient = (1.21 – 1.08) = ± 0.1 cms-2
Round to 1 sf
State the relationship between the variables
Conclusion
Using: a = 2x gradient = 2.4 cms-2 Theoretical gradient = ??? How does the experimental gradient value compares ??? with the theoretical value.
Theoretical say it was 2.8 cms-2
How does the experimental value compare?

14. State the relationship between the variables
Conclusion =
This statement shows
linear relationship between speed and time
error in the GRADIENT
error in the INTERCEPT
Try and include units (be careful about the y axis intercept units)