[ ] initial position: 32 meters final time: 5 seconds initial time: 4 seconds velocity in interval: 18.0 meters per second [] ] Select other elements from the position and time lists and get as close as \# possible to time =9.25 seconds final_position = position_list[] \# change the element number initial_position = position_list[18] \# this one too final_time = time_list[] \# make sure element numbers are the same initial_time = time_list[] \# as for the positions velocity = calculate_velocity(final_position, initial_position, final_time, initial_time) print('final position: ', final_position, 'meters') print('initial position: 'initial_position, 'meters') print() print('final time: ', final_time, 'seconds') print('initial time: ', initial_time, 'seconds') print() print('velocity in interval:', velocity, 'meters per second') final position: 338 meters initial position: 8 meters final time: 13 seconds initial time: 2 seconds velocity in interval: 30.0 meters per second Following the rules of calculus, the derivative of position with respect to time is: dtdx=dtd(At2)=2At. Since we decided that A=2m/s2, v=dtdx=4m/s2t. Notice that, since the units of time are seconds, the units of our derivative are meters per second, as expected from a velocity. Notice also that the velocity is a function of the time, so you could write it as v(t)=4m/s2t. The longer you let your object go, the faster it will be moving at the end. Another way to say this is that the object is accelerating. Analytically, the velocity of the object at 9.25 seconds is: v(9.25s)=4.00m/s29.25s=37.00m/s 1. Run the code below, which calculates the velocity between a given change in position and change in time. Then play around with the selected elements until you find a pair that gets close to t=9.25 seconds. What is the velocity and how does it compare to the analytical velocity? 2. Repeat Exercise 2.1 but now using the 'finer' position list and time list. Can you get closer to t=9.25 seconds? What is the velocity and how does it compare to the analytical velocity