# Will a sprinter's speed keep increasing all the time?

1. May 13, 2010

### yasar1967

when a sprinter starts running he applies force to overcome fraction and air drag. is his speed keeps going up as F=ma governs to? if he's stamina was enough to fuel him for hours will his speed will keep going up and up even though he applies a constant force until the air drag force becomes so big that his muscles' force merely counteracts the fraction plus drag and drops to zero thus reaching constant speed?
What if hypothetically he runs in space on a surface which an artificial fraction made?
I'm aware of the limit due to reaching speed of light and mass increase. I'm not going that far.

2. May 13, 2010

### Nabeshin

Air friction roughly scales with the square of the moving object's speed, so a doubling of the runner's speed quadruples the amount of work he needs to put in to maintain this speed. I'm not sure if this is the limit, though, as I don't know much about running. However I am more inclined to believe that actual sprinters are more limited by how fast they can move their legs, since the legs have quite a bit of inertia on their own.

3. May 13, 2010

### hotvette

I'm of the opinion that there is an asymptotic limit, but the tail could be very long. In addition to more specialized physical training and medical advances, environmental factors will increamentally help (i.e. advances in footgear, running surfaces, and clothing).

4. May 13, 2010

### Staff: Mentor

But in addition, work (power, actually), is a linear function of speed even if force is held constant, so actually, the power the runner has to expend is a cube function of speed. Doubling the speed means 8x the power. Four times the force times twice the speed.
Agreed.