One of the most popular events at the 1998 Winter Olympics in Nagano, Japan, was the luge. In this event, competitors lie on their backs and slide down an iced track on small sleds. At times, luge riders travel more than $120$ km per hour!

During one particular run, a competitor from Norway had the times and distances listed in the table below. The track is $1200$ m long. Enter the data points into your graphing calculator and then complete parts (a) through (c) below.

1. Determine the average velocity of the competitor during the run.

   Hint (a):

   average velocity given position $=$ AROC $=$ slope of the secant line

2. The graph of the distance can be modeled by $s(t)=$$0.000145t^4-0.0246t^3+$$1.315t^2-15.808t+$$5.582$ using a quartic regression. Use your curve to approximate the velocity at $t = 96$ sec, when the athlete completed the race. Convert your result to km/hr. Is your result reasonable?

   Hint (b):

   If $y =$ distance, what does $y^\prime =$ ?

3. Graph the first derivative of your curve of best fit to represent the velocity. Explain its shape. What happens during the course of the run that helps explain its shape?

   Hint (c):

   Does the Norwegian competitor ride his luge at a constant rate? How can you tell?