# Who's faster?

### Ryan Lochte or Michael Phelps?

## Background Information

In the 2012 London Olympics, Ryan Lochte and Michael Phelps swam in the same race, the 400 meter individual medley. Lochte won the gold medal with a time of 4:05.18. Phelps came in fourth place with a time of 4:09.28.

## Lochte's Velocity

The overall average velocity for Lochte was 1.63 m/s. But for each individual strokes used in this event his velocities were:

Butterfly: 1.82 m/s

Back: 1.62 m/s

Breast: 1.44 m/s

Free: 1.71 m/s

All of these velocities were found by using the formula of v = x/t for v being velocity, x being distance, and t being time.

His final velocity would be 3.26 m/s. I figured this velocity by using the formula Vf = 2v.

## Lochte's Acceleration

The formula for acceleration is a = (Vo + Vf)/t. Vo stand for original velocity which would be zero since he isn't moving and Vf stands for final velocity which is 1.63 m/s. So his acceleration would be .0066 m/s2 (seconds squared).

## Phelps' Velocity

The overall average velocity for Phelps was about 1.6 m/s. Michael Phelps time are approximated because they didn't seem to be posted on the internet. But for the individual strokes his velocities were:

Butterfly: 1.81 m/s

Back: 1.56 m/s

Breast: 1.49 m/s

Free: 1.59 m/s

All of these velocities were found by using the formula of v = x/t for v being velocity, x being distance, and t being time.

The final velocity for him would be 3.2 m/s. I figured this out by using the formula of Vf = 2v.

## Phelps' Acceleration

The formula for acceleration is a = (Vo + Vf)/t. Vo stand for original velocity which would be zero since he isn't moving and Vf stands for final velocity which is 1.6 m/s. So his acceleration would be .0064 m/s2 (seconds squared).

## Conclusion

In conclusion Ryan Lochte was the faster swimmer in this particular event. Only by a mere 4.1 seconds. But in the past Michael Phelps has been faster so I think the results depend on the kind of day the swimmers are having.

## *Lochte's times are exact but Phelps' times are approximated.*

## Key

t = time

v = velocity

x = distance

a = acceleration

Vo = original velocity

Vf = final velocity