How Far Does a Sprinter Run During Acceleration in a 100m Dash?

[nathan scott]

Homework Statement

In the 100 m dash a sprinter accelerates from rest to a top speed with an acceleration whose magnitude is 2.68 m/s². After reaching top speed, he runs remainder of race with constant velocity. If total race is run in 12.0s, how far does he run during the acceleration phase?

Homework Equations

d₁= 1/2*2.68 m/s²*t²
d₂= vt = 2.68 m/s²*t*12.0s - t

The Attempt at a Solution

Not knowing if the above equations are correct I tried d₁+d₂=100m.
I multiplied everything, moved the 100m to the other side and tried the quadratic formula. I don't think I came out with the correct answer. I got approx. t= 3.5 or t= about 18. Any suggestions

 

[nathan scott]

Nevermind. I've finally figured out my errors.