# How far does he run during the acceleration phase?

1. Sep 7, 2006

### dvbballgurl11

If anyone could help it would be greatly appreciated!!!! 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?

2. Sep 7, 2006

### dmoravec

well I'd start by setting up the equations of motion in two parts: the accelaration phase and the constant speed phase:
ie: for 0<t<t(a) s(t) = 3.5/2 * t^2 [t(a) is the time they stop accelarating]..
do the same for the constant speed (its a bit more complicated) and using your known values see what you can do

3. Sep 7, 2006

### dvbballgurl11

hey i tried doing that but cannot seem to come up with the right answer. any ideas?

4. Sep 7, 2006

### dmoravec

well, when you are done accelarating what is your speed? (using t(a) as a variable) and how far have you gone? (again using t(a) and the 1st equation)

5. Sep 7, 2006

### dvbballgurl11

i dont know i keep getting confused on what to plug in where. any chance on getting help setting up the equations?

6. Sep 7, 2006

### dmoravec

something like this
0<t<t(a) s(t)=3.5/2 t^2
t(a)<t<t(f) s(t) = [3.5*t(a)]*[t-t(a)] + 3.5/2*t(a)^2