Careful measurements have been made of Olympic sprinters in the 100 meter dash. A simple but reasonably accurate model is that a sprinter accelerates at 3.6 m/s² for 3 1/3 s, then runs at constant velocity to the finish line.

a. What is the race time for a sprinter who follows this model?

b. A sprinter could run a faster race by accelerating faster at the beginning, thus reaching top speed sooner. If a sprinter’s top speed is the same as in part a, what acceleration would he need to run the 100 meter dash in 9.9 s?

c. By what percent did the sprinter need to increase his acceleration in order to decrease his time by 1%?