For the first 4 seconds of a race, a sprinter accelerates at a rate of 3 meters per second per
second (3 m/sec^2). He then continues to run at the constant speed that he has attained for the
rest of the race.
a. Write a piecewise function to express the sprinter's velocity v(t) as a function of time.
b. Find v(2), (4), and v(6).
c. Write a piecewise function to express the sprinter's position s(t) as a function of time.
d. How far does the sprinter run during the first 4 seconds of the race?
e. How long will it take the sprinter to run 100 m?
