What is the sprinter's speed at the finish line?

[pingpong240]

Here is the problem I am trying to do:
A sprinter can accelerate with constant acceleration for 3.8 s before reaching top speed. He can run the 100 meter dash in 15.0 s. What is his speed as he crosses the finish line?

I'm currently trying to break this into two separate intervals. I believe the variables I am trying to find are the acceleration for the first interval, the distance that the sprinter beings running at top speed, and of course that speed. I'm trying kinematic equations but I always seem to end up with two unknowns in the same equation. A little push in the right direction is much appreciated! : )

 

[hage567]

Are you making use of the fact that d1+d2=100, and t1+t2=15s? It would be helpful if you showed more of your work.

 

[Mindscrape]

You are already headed in the right direction. You know there will be two functions of positions, one with acceleration, and one with a constant velocity. Together these will add up to the total distance. Two equations, and two unknowns (acc and vel).

 

[pingpong240]

OK...sounds like I should consider a system of two equations and possibly combine them into one with variables that I know...

 

[Mindscrape]

Well yes, you must have at least two equations if you have two unknowns. As far as I know there aren't infinite solutions to the velocity vector. What did you come up with?

 

[pingpong240]

No answer yet. I just expressed velocity over the first interval as 3.8a, now I am trying to represent the change in distance over that first interval in terms of a as well, and hopefully solve for a. Is this the right way so far?

EDIT: Didn't work for me.

 

[pingpong240]

Never mind I figured it out. Thanks for your help! ;)