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) Position (m) 0 0 1 -1 2 -2 3 -4 4 -7 5 -15 (a) Using a calculator or computer program, find the best-fit quadratic curve to measure the position of the sensor (in m) as a function of t, the time (in s) after the sensor is dropped. (Round all numerical values to four decimal places.) (a) Using a calculator or computer program, find the best-fit quadratic curve to measure the position of the sensor (in m) as a function of t, the time (in s) after the sensor is dropped. (Round all numerical values to four decimal places.) p(t) = -0.23147³ +0.9683/2-2.0463t+ 0.0873 (b) Find the derivative of the position function from part (a). p'(t)= -0.694412 +1.9365t-2.0463 x Explain the physical meaning of the derivative. The derivative of the position function gives the velocity ✓ ✓ of the sensor as a function of t. (c) Find the second derivative of the position function from part (a). p"(t) = -1.3889t+1.9365 x Explain the physical meaning of the second derivative. ✔ as a function of t. It is increasing velocity X upward The second derivative of the position function gives the acceleration of the sensor