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

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%

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%

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%

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

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 + 0.05 (s) d + 10% (cm)

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 + 0.05 (s) d + 10% (cm)

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 + 0.05 (s) d + 10% (cm)

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!

Calculate gradients & record intercepts for BOTH lines Line of best fit Line of worst fit Line of Best fit: Intercept = -0.29 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

State the relationship between the variables Line of best fit: Intercept = -0.29 cm Gradient = 1.21 cms-2 Line of worst fit: Intercept = 0.5 cm Gradient = 1.08 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?

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)