(a) Usain St Leo Bolt is the fastest human in recorded history. His top speed is 12.27 m/sec. (i) (Part 1a) If Bolt maintains his top speed over a 5-second interval, how much distance does he travel in that time? (ii) (Part 1b) Draw a graph of Bolt's velocity function over the 5 second interval from part 1(a)(i), assuming the start of the interval occurs at t = 5 and the end occurs at t = 10. Label your axes. Leave space to add to your graph for 0 S ts 5. (iii) (Part 1c) The region between the graph form part 1(a)(ii) and the t-axis, from t = 5 to t= 10, forms a rectangle. What is the area of the rectangle? What is the relationship between the area and your answer to part 1(a)(i)? (b) It takes roughly 5 seconds for Usain Bolt to obtain his top speed. The following table shows approximate velocities over the first 5 seconds of Usain Bolt's world record File Preview )0 meter dash in the Berlin World Championships in 2009. time (sec) 0 1 2 3 4 5 velocity (m/sec) 0 6 10 11 11.7 12.27 (i) (Part 2a) Draw a graph of Usain Bolt's velocity from t = 0 to t = 5, and connect it to the graph from 1(b). (ii) (Part 2b) Using the above data, make an educated guess about how much distance Bolt traveled in the first second, from time 0 to time 1 (There's more than one reasonable answer). (iii) (Part 2c) About how much area is between the velocity graph and the t-axis, from t = 0 to t = 1? Is there a relationship between this area and your answer to part 2(b)(ii)