Here's an example script in Python for fitting a quadratic polynomial to measured data using least-squares regression analysis and using the polynomial coefficients to determine the acceleration, initial speed, and position of a particle:
import numpy as np
# Example measured data (time and position)
time = np.array([0, 1, 2, 3, 4])
position = np.array([0, 1.2, 4.5, 10.1, 17.9])
# Fit a quadratic polynomial to the data using least-squares regression
coeffs = np.polyfit(time, position, 2)
# Extract the coefficients for the quadratic polynomial
a = coeffs[0]
b = coeffs[1]
c = coeffs[2]
# Compute the acceleration, initial speed, and position of the particle
acceleration = 2 * a
initial_speed = b
initial_position = c
# Print the results
print("Quadratic polynomial coefficients: a = {:.2f}, b = {:.2f}, c = {:.2f}".format(a, b, c))
print("Acceleration: {:.2f}".format(acceleration))
print("Initial speed: {:.2f}".format(initial_speed))
print("Initial position: {:.2f}".format(initial_position))
In this script, the numpy.polyfit() function is used to fit a quadratic polynomial to the measured data using least-squares regression. The resulting polynomial coefficients are then used to calculate the acceleration, initial speed, and initial position of the particle. Finally, the results are printed to the console.
Note that you will need to modify this script to use your own measured data, and adjust the formatting of the output to suit your needs.