How Long Does a Sprinter Accelerate Before Reaching Top Speed?

[Cliborpimus]

Homework Statement

The sprinter completes 200m in 19.3sec. When the starting pistol fires he accelerates constantly until he reaches his top speed of 13.4m/s. He then holds speed till the 200m point. At what time did he stop accelerating and how many meters did he cover before reaching top speed.

Homework Equations

Vf=Vi+ at
Xf=Xi+(1/2)(Vi+Vf)t
Xf=Xi+Vi t + (1/2)at^2
Vf^2=Vi^2 +2a (Xf-Xi)

The Attempt at a Solution

I know I have solved something like this before but it's been about 4 years since I've been in school and just can't seem to remember. I feel no matter what I do I am always short a variable. I have tried breaking it down into two different problems but I just can't seem to get it.

 

[haruspex]

Homework Statement

The sprinter completes 200m in 19.3sec. When the starting pistol fires he accelerates constantly until he reaches his top speed of 13.4m/s. He then holds speed till the 200m point. At what time did he stop accelerating and how many meters did he cover before reaching top speed.

Homework Equations

Vf=Vi+ at
Xf=Xi+(1/2)(Vi+Vf)t
Xf=Xi+Vi t + (1/2)at^2
Vf^2=Vi^2 +2a (Xf-Xi)

The Attempt at a Solution

I know I have solved something like this before but it's been about 4 years since I've been in school and just can't seem to remember. I feel no matter what I do I am always short a variable. I have tried breaking it down into two different problems but I just can't seem to get it.

Your standard relevant equations involve six variables. Which of these are known from the question, and which do you have to find?