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**1. 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 3.8 m/s2 for 3.26 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 9.61 s?

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

(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 9.61 s?

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

**2. Homework Equations**

Vf=Vi+at

Sf=Si +Vi*t+.5*a*t^2

**3. The Attempt at a Solution**

ok i am able to get part (a):

i started by finding the velocity for the rest fo teh race after the acceleration:

Vf=0+((3.8)(3.26))=12.388 m/s

then i found how far he traveled during the acceleration:

Sf=0+0+.5((3.8)(3.26))=20.19m

next i found how much time it took to complete the race from t=3.26s:

100=20.19+(12.388)t+.5(0)t^2

100-20.19=12.388t

t=6.44s

finally:

t(total)= 3.26+6.44= 9.7s

now i have been looking at the last two parts and i have no idea where to start.