Setting up acceleration problem

[dvbballgurl11]

Help Please!

I could really use someone's help with finding the answer or setting up the equations!
A sprinter accelerates from rest to a top speed with an acceleration whose magnitude is 3.50 m/s2. After achieving top speed, he runs the remainder of the race without speeding up or slowing down. The total race is one hundred meters long. If the total race is run in 17.00 s, how far does he run during the acceleration phase?

Thank You!

 

[berkeman]

What equations do you use to relate acceleration, velocity and distance? You need to kind of split the run into two pieces (the second is all at the constant velocity), and define the distance where this transition happens as x (somewhere between 0 and 100m, obviously). And that will correspond to a time t when the sprinter passes the point. Use those equations and the variables x and t to figure out the runner's velocity as a function of time, and the answer to the question is the x that you find.

 

[radou]

(1)...s1 = (a*t1^2)/2 = 1.75*t1^2
(2)...s2 = v*(17-t1) = 3.5*t1*(17-t1) = 59.5*t1 - 3.5*t1^2
(3) s1+s2=100 => -1.75*t1^2 + 59.5*t1 - 100 = 0 => t1 = 1.77 seconds => s1 = 1.75*1.77^2 = 5.48 m

 

[dvbballgurl11]

i don't know the equations to use. any chance of you helping me set them up?

 

[dvbballgurl11]

Thank You!

 

[berkeman]

radou,

We are not supposed to give answers to homework questions here in the HW forums. Please re-read the guidelines for the HW forums -- that limitation is made very clear. We are allowed to give hints and help guide students to figuring out the answers, but not just post them. Think about it, what does the OP learn when they can just copy and paste your answer into their homework? It would be best if you can edit your post to turn it into hints instead.

 

[berkeman]

Thank You!

Oops. Too late. Please keep the HW forum guidelines in mind next time radou.

 

[radou]

Sorry, I'll keep that in mind!