# Sprinter's Power Output

1. May 4, 2010

### tangibleLime

1. The problem statement, all variables and given/known data
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?

2. Relevant equations
$$x=x_0 + v_0 t + \frac{1}{2}at^2$$
$$\vec{F}=ma$$
$$v=v_0 + at$$
$$KE=\frac{1}{2}mv^2$$
$$P=\frac{\Delta E}{\Delta t}$$

3. The attempt at a solution
For part A, I first used $$x=x_0 + v_0 t + \frac{1}{2}at^2$$ to find the acceleration of the sprinter:

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

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

$$\vec{F}=ma$$
$$\vec{F}=48(1.726)$$
$$\vec{F}=82.9 N$$

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 $$1.7 sec$$:

$$v=v_0 + at$$
$$v=0 + (1.726)(1.7)$$
$$v=2.934 m/s$$

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

$$KE=\frac{1}{2}mv^2$$
$$KE=\frac{1}{2}(48)(2.934)^2$$
$$KE=206.6 J$$

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.

$$P=\frac{\Delta E}{\Delta t}$$
$$P=\frac{206.6}{1.7}$$
$$P=121.55 W$$

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.

2. May 4, 2010

### tangibleLime

Nevermind, I figured it out.

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