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## Homework Statement

in a women's 100-m race, accelerating uniformly, Laura takes 2.00 s and Healan 3.00 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. What is the acceleration of each sprinter?

## Homework Equations

vf = vi + at

xf = xi + .5(vi + vf)t

xf = xi + vit + .5at^2

vf^2 = vi^2 + 2a(xf-xi)

where vf, vi, xf and xi are final and initial velocity and horizontal position (respectively)

## The Attempt at a Solution

xf = xi + vit + .5at^2

100 = (0) + vit + .5a(10.4)^2

9.62 = vi + 5.4a

avg velocity = 100/10.4 = 9.61 m/s

a = v/t

a (Laura) = 9.61 / 2 = 4.8 m/s^2

a (Healan) = 9.61 / 3 = 3.2 m/s^2

my books answers are 5.32 m/s^2 for laura and 3.75 m/s^2 for healan. i don't know how to get there...

I've tried using all of the above equations, but I can't get anything to work out because I have too many unknowns (vf, vi, and a). For awhile I tried using 0 as the value of vi and xi, but that didn't work out, either. I can't figure out how to use the information about the time each person reached maximum speed (or if it should be used at all).

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