In a women's 100-m race, accelerating uniformly, laura takes 1.96 s and healan 3.11 s to attain their maximum speeds, which they each maintain for the rest of the race. they cross the finish line simultaneously, both setting a world record of 10.4 s. (a) what is the acceleration of each sprinter?

First we write the kinematic equations
 a
 v = a * t + vo
 r = (1/2) at ^ 2 + vo * t + ro
 We have then that:
 (10.4 - t) = time that they run at their maximum speed
 For Laura:
 d = (1/2) at ^ 2 + (at) (10.4 - t)
 100 m = (1/2) a (1.96) ^ 2 + [(1.96) a] (8.44)
 100 = 1.9208a + 16.5424a
 100 = 18.4632a
 a = 100 / 18.4632 = 5.42 m / s ^ 2
 For Healen:
 100 = (1/2) a (3.11) ^ 2 + [(3.11) a] (7.29)
 100 = 4.83605a + 22.6719a
 100 = 27.50795a
 a = 100 / 27.50795
 a = 3.64 m / s ^ 2
 
 the acceleration of each sprinter is
 Laura: 5.42 m / s ^ 2
 Healen 3.64 m / s ^ 2