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6. The table below lists time (secs) and speed (ft per sec) of a model rocket as measured at several time points after launch using an instrument with uncertainty +/- 5 fps. Time (s) 1 10 50 100 150 Speed (fps) 88 90 130 120 110 a) Use linear and cubic spline interpolation to estimate the speed when the time was 120s. b) Fit the data with polynomial functions ranging in order from 1 to 4 (hint: use polyfit). In each of the four cases, plot the fitted polynomial as a smooth blue curve along with the data represented as red circles. (Hint: generate a new vector of time values containing ~100 elements, and use polyval to determine the corresponding theoretical speeds.) In addition to your code, submit the plot for the polynomial order that you believe gives the best reasonable description of the data, along with an explanation for your reasoning. Include in your explanation a comparison of the predicted speed at 120 sec for each of the polynomial models as well as for the interpolated values in part (a) above. c) Estimate the total distance traveled during the 150 secs (hint: area under the curve), first using trapezoidal rule on the measured data, and second by applying the built-in integral function to your polynomial model from part (b). (Note that you will need to define your polynomial model as an anonymous function, using polyval and the coefficient array.) d) Create a plot of the acceleration of the rocket as a function of time. Remember that this is best done using the smoothed model rather than the measured data