How Much Power Does a Sprinter Generate in a Race?

[tangibleLime]

Homework Statement

A 48.0 kg sprinter, starting from rest, runs 46.0 m in 7.30 s at constant acceleration.

a) What is the magnitude of the horizontal force acting on the sprinter?

b) What is the sprinter's power output at 1.70 s?

Homework Equations

[tex]x=x_0 + v_0 t + \frac{1}{2}at^2[/tex]
[tex]\vec{F}=ma[/tex]
[tex]v=v_0 + at[/tex]
[tex]KE=\frac{1}{2}mv^2[/tex]
[tex]P=\frac{\Delta E}{\Delta t}[/tex]

The Attempt at a Solution

For part A, I first used [tex]x=x_0 + v_0 t + \frac{1}{2}at^2[/tex] to find the acceleration of the sprinter:

[tex]x=x_0 + v_0 t + \frac{1}{2}at^2[/tex]
[tex]46=0 + 0(7.3) + \frac{1}{2}a(7.3)^2[/tex]
[tex]a=1.726 m/s^2[/tex]

With the acceleration, I stuck it into Newton's Second Law and found the force.

[tex]\vec{F}=ma[/tex]
[tex]\vec{F}=48(1.726)[/tex]
[tex]\vec{F}=82.9 N[/tex]

My answer for part A was correct.

Part B is where I am having some difficulties. First I got the velocity of the runner at [tex]1.7 sec[/tex]:

[tex]v=v_0 + at[/tex]
[tex]v=0 + (1.726)(1.7)[/tex]
[tex]v=2.934 m/s[/tex]

I then calculated the amount of work done by calculating the kinetic energy, which I used because the sprinter is running and in motion.

[tex]KE=\frac{1}{2}mv^2[/tex]
[tex]KE=\frac{1}{2}(48)(2.934)^2[/tex]
[tex]KE=206.6 J[/tex]

Then to calculate power, I took the change in the kinetic energy (0 J to 206.6 J) and divided it by the change in time.

[tex]P=\frac{\Delta E}{\Delta t}[/tex]
[tex]P=\frac{206.6}{1.7}[/tex]
[tex]P=121.55 W[/tex]

That answer was marked incorrect. I then tried to add the horizontal force (the answer to part A), which added up to 204.45 W and that was also incorrect.

Any help would be greatly appreciated.

 

[tangibleLime]

Nevermind, I figured it out.

I did P=F*v which gave me the correct answer.