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 θ(t) and φ(t), respectively, where 0 ≤ t ≤ 4 and t is measured in minutes (see figure). These angles are measured in radians, where θ =  φ = 0 represent the starting position and θ = φ = 2π represent the finish position. The angular velocities of the runners are θ'(t) and φ'(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 θ(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 φ(t) = πt(8 - t)/8. What is his angular velocity at t = 2 and at what time is  is angular velocity the greatest?

Transcribed Image Text:

Finish 2п- Juan, p(t) 4(t) Ө() Start IT Jean, 0(t) Finish + + Circular track Start 1 3 4 Time (minutes) Angular position (radians) +