(Solved): First Finite-Divided-Difference Methods You have recently joined the Ferrari Formula One (F1) team ...

First Finite-Divided-Difference Methods You have recently joined the Ferrari Formula One (F1) team. The team wants an easy method to take camera data to calculate the velocity of the driver during a race. Your co-worker has developed a function that will take all the camera data and return it as a set of positional data \( (x) \) in kilometers relative to the start of the race ( \( x=0 \mathrm{~km} \) implies the starting position of the car at \( t=0 \mathrm{~s}) \). a) Using the most accurate numerical method for each individual calculation by hand compute the velocity in kilometers per hour (KPH) for each point in time from the data below. b) Based on the speeds you calculated in part a), draw what you think the start of this race track looks like. Label the \( x \) points from the table in part a) and give a justification for your race track. Note 1: F1 cars can accelerate from 0 to \( 100 \mathrm{KPH} \) in about \( 2.4 \) seconds, corner at speeds of 300 \( \mathrm{KPH} \), and have top speeds around \( 360 \mathrm{KPH} .{ }^{1} \) Also, assume there were no crashes on the track and this is a sprint. (A sprint is a race with only one lap, and the start and end of the race do not have to be in the same location.) Note 2: Do not take a long time on this. This is supposed to be a fun thought exercise.