my 2 T The centripetal force of an object of mass m is given by F (r): rotation and r is the distance from the center of rotation. a. Find the rate of change of centripetal force with respect to the distance from the center of rotation. b. Find the rate of change of centripetal force of an object with mass 1000 kilograms, velocity of 13.89 m/s, and a distance from the center of rotation of 200 meters. where v is the speed of For the following exercise, consider an astronaut on a large planet in another galaxy. To learn more about the composition of this planet, the astronaut drops an electronic sensor into a deep trench. The sensor transmits its vertical position every second in relation to the astronaut's position. The summary of the falling sensor data is displayed in the following table. Time after dropping (s) 0 1 2 3 4 5 Position (m) 0 -1 -2 -5 -7 -14 a. Using a calculator or computer program, find the best-fit quadratic curve to the data. b. Find the derivative of the position function and explain its physical meaning. c. Find the second derivative of the position function and explain its physical meaning.