# Physics of a runner (Constant Acceleration/ constant velocity)

1. Feb 9, 2010

### Cllzzrd

1. The problem statement, all variables and given/known data
"The 100- dash can be run by the best sprinters in 10.0 . A 64- sprinter accelerates uniformly for the first 41 to reach top speed, which he maintains for the remaining 59 ."

What is the average horizontal component of force exerted on his feet by the ground during acceleration?

What is the speed of the sprinter over the last 59 of the race (i.e., his top speed)?

2. Relevant equations

F=ma
v=Vi+at
Xo=Xi+Vit+.5at^2
Vo^2=Vi^2+2a(Xo-Xi)
3. The attempt at a solution

I honestly have no idea how to even start this problem.

For the part where the runner is accelerating, here is what I have
Xi-0
Xo-41
Vi-0
Vo-?
a-?
t-?

Which is not much... For when he is at a constant speed, here is what I have.

Xi-41
Xo-100
Vi-?
Vo- ? (the same as Vi, as he is at a constant velocity)
a-0
t-?

So Xo=.5at
41=.5at

Vo=at
a=Vo/t

Vo^2=Vi^2+2a(Xo-Xi)
Vo^2=0+2(Vo/t)(41)

I am completely stuck... I have no idea where to go from here. Am I just looking at it wrong, or is there some important part that I missed?

2. Feb 9, 2010

### willem2

just assume the topspeed is equal to v. Compute the total time taken as a function of v and set that equal to 10 seconds.