Finding acceleration of two sprinters from race data

[HMPARTICLE]

1. The problem statement.
Setting new world records in a 100-m race, Maggie and Judy cross the finish line in a dead heat, both taking 10.2s. Accelerating uniformly, Maggie took 2.0s and Judy 3s to attain maximum speed, which they maintained for the rest of the race.

What was the acceleration of each sprinter?

2. Homework Equations

https://www.physicsforums.com/attachments/70692These guys
3. Attempt.

I have no idea where to start as each equation is useless on its own. Each sprinter has a different maximum velocity. A poke in the right direction is all I need. I've tried stating that the position Maggie obtains at the point she reaches her maximum speed is equal to 0.5 x a x t^2 which doesn't actually get me anywhere as I don't know her max speed or her acceleration.

 

[Orodruin]

You know what the speed is in terms of the acceleration as a function of time. How do you relate this to the distance covered as a function of time?

 

[HMPARTICLE]

This is as far as I have gone :(. Thanks for the reply. Using these equations I'm sure I should be able to find the acceleration? Am I suppose to use the fact that it took them both 10.2 seconds?

 

[Orodruin]

Try writing down separately the distance covered during the accelerating phase and that covered during the constant speed phase (what is the constant speed in terms of the acceleration? how long does the constant speed phase last?) Adding them together you should get 100 m.

 

[HMPARTICLE]

Am I in the ball park? I'm sorry about all the pictures, I'm on a tablet.

 

[dauto]

You need to organize your thoughts. There are two separate motions here. 1st there is the accelerated motion. write down the equations for position and velocity for that motion assuming they start from rest at initial position x=0. Then there is the 2nd motion which is uniform motion at constant speed. Write down the formula for the position and velocity for that motion keeping in mind that the starting position of the 2nd motion is the final position of the 1st motion.

 

[HMPARTICLE]

Thanks guys! All done! Organisation was the key.