A race Jean and Juan run a one-lap race on a circular track. Their
angular positions on the track during the race are given by the
functions u(t) and w(t), respectively, where 0≤ t≤ 4 and t is
measured in minutes (see figure). These angles are measured in
radians, where u = w = 0 represent the starting position and
u = w = 2π represent the finish position. The angular velocities
of the runners are u′(t) and w′(t).
a. Compare in words the angular velocity of the two runners and
the progress of the race.
b. Which runner has the greater average angular velocity?
c. Who wins the race?
d. Jean’s position is given by u(t) = πt2/8. What is her angular
velocity at t = 2 and at what time is her angular velocity the
greatest?
e. Juan’s position is given by w(t) = πt18 - t2/8. What is his
angular velocity at t = 2 and at what time is his angular velocity the greatest?
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