Energy and Power

$$$$P = W/t	Power is the amount of work done over a given amount of time.
$$W =F(x)	Work is the force of thrust times the distance over which the force is exerted.

Using the above equations and substituting our Work equation into our Power equation we can get the following equation:

$$Power = F(x)/t
 
where power is the force of thrust multiplied by the distance over time.

$Velocity = \left(\frac{x}{time}\right)$

Velocity is distance traveled over time.

Using the above velocity equation and plugging that into our new power equation we get

$$Power = F(v)

where power is the force of thrust multiplied by the velocity of the swimmer.

$$F=bv

If the force of thrust is equal to the magnitude of the force of drag then the force of thrust is the velocity multiplied by a constant.

In the above equation we are assuming the swimmer is moving at a constant speed, so the force of thrust would equal the magnitude of the force of drag. 'b' is a constant dependent on the shape of the swimmer and the amount of drag their suit, skin, and hair creates. Using that equation in our power equation we get that

$$Power = bv^2

where power is velocity squared multiplied by a constant.

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If we use the equations above, we can solve for how much power is created by a swimmer swimming 50 yards of the freestyle stoke.

If the distance the swimmer is traveling is 45.72 meters and she does it in 27.20s, the average velocity for the swimmer would be

$$Velocity = 45.72m/27.20s = 1.68m/s

If we plug this average velocity into our power equation we get

$$Power = b(1.68m/s)^2

If we use 247.9kg/s (constant for world record speed) as our constant we get that

$$Power = (247.9 kg/s)(1.68 m/s)^2 = 699.67W

699.67W of power are created by a swimmer swimming 50 yards in 27.20 seconds.
$Power = {\left(1.68\frac{m}{s}\right)}^{2}\left(247.9\frac{kg}{s}\right) = 699.67 Watts$

https://thenounproject.com/term/light-bulb/16966/

All this power created by the swimmer could power a 60W light bulb for 11 hours and 40 minutes.