Using statistics tool on acceleration vs. time graph you read on the screen the

Question

Using statistics tool on acceleration vs. time graph you read on the screen the mean value of acceleration a=0.131 m/s2 and standard deviation =0.0243 m/s2 and you counted the number of measurements in the sample to be N=6.

Happy with your results you proceed to confirm your findings by applying a quadratic fit to your position vs. time graph. Just like discussed in the introductory videos the fit tool returns both the value of the fit parameters and the associated error. The quadratic fit yielded the function Ax2+Bx+C with the following values of parameters and errors: A =0.0655 ± 0.0005, B =0.0500 ± 0.0086, and C =0.325 ± 0.0099. Keep 3 significant figures in your final result for the acceleration, calculate the average acceleration and the corresponding standard error from the parabolic fit parameters above.

HINTS:

1) While the generic quadratic expression is a function of x what is it really a function of on your graph?

2) Now establish the relation between the fit parameters and the physical quantities such as acceleration, initial velocity and initial position.

3) Review the section on propagation of error in your Appendix or Lab 1 notes. If a measured quantity is multiplied by a constant what happens to its error? Does it make sense that a relative error of a measured quantity does not change when the quantity is multiplied by a constant?

Explanation / Answer

Here, displacement s = At2 + Bt + C

Average Acceleration a = d2s/dt2

= 2A

=2×0.0655 = 0.131

Standard error = delta a = 2*deltaA

= 2×0.0005 = 0.001 m/s^2

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