Question

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?

Answer 1

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
Answer:
the acceleration of each sprinter is
Laura: 5.42 m / s ^ 2
Healen 3.64 m / s ^ 2