# Speed of a Retired Basketball Player: Charles Barkley and Dick Bavetta

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## Abstract

The purpose of this project is to determine the velocity and the acceleration of both Charles Barkley and Dick Bavetta in their race against each other the 2007 NBA finals helftime show.

## Introduction

Velocity is the rate of change of displacement. It is measured in meters per second. The scalar absolute value of velocity is speed. The formula used to find velocity is

v_{ave} = d/t

Acceleration is the rate of change of velocity. It is measured in meters per second squared. The formula used to determine acceleration is

a = (v_{f}–v_{i})/t

During uniform accelration, v_{f} is twice v_{ave}. The average velocity would be equal to the intial velocity plus the final velocty divided by two. Since the initial velocity at the begining of the race is zero, the acceleration would be equal to twice the average velocity, divided by the time.

a = 2 v_{f}/t

During all-star weekend this past year in Las Vegas, Charles Barkley (age 44) and Dick Bavetta (age 67) competed in a 2½ lap race up and down the court. In this project we will determine the velocity and the acceleration of Charles Barkley and Dick Bavetta during their race.

Dick Bavetta (Source: viewimages.com)

## Procedure

- Watch a video of the race between Charles Barkley and Dick Bavetta.
- Determine the length in meters of a standard basketball court.
- Determine the total distance ran.
- Determine the time it took both runners to finish the race.
- Use the distance and the time to find the velocity of each runner.
- Use the velocity at rest and the velocity at the end of the race to determine the acceleration.

## Analysis

A standard size basketball court in the NBA is 94 ft long and 50 ft wide. In this race, Barkley and Bavetta had to run 2½ laps up and down the court. Total distance ran was 235 ft. When converted to meters, the distance ran was 71.63 meters.

### Charles Barkley

Charles Barkley completed the race in 21 seconds. To find his velocity we divide the distance by the time.

v = d/t

v = (71.63 m)/(21 s)

v = 3.41 m/s

Next we needed to find Barkley's acceleration. At t = 0, Barkley's velocity was 0 m/s because the at the beginning of the race he started from rest. When he completed the race at t = 21 s, his velocity was 3.41 m/s. To find the acceleration we multiply the final velocity by two and divide that number by the time.

a = 2 v_{f}/t

a = 2 (3.41 m/s)/(21 s)

a = 0.325 m/s^{2}

### Dick Bavetta

Dick Bavetta on the other hand completed the race in 22 seconds. To find his velocity we once again divide the distanced by the time.

v = d/t

v = 71.63 m/22 s

v = 3.26 m/s

Next we needed to find Bavetta's acceleration. At t = 0, Bavetta's velocity was 0 m/s because the at the beginning of the race he started from rest. When he completed the race at t = 22s, his velocity was 3.26 m/s. To find the acceleration we multiply the final velocity by two, which gives us the average velocity. We then divide this number by the time it took Bavetta to finish the race.

a = 2v_{f}/t

a = 2(3.26 m/s)/ (22 s)

a = 0.296 m/s^{2}

## Conclusion

Charles Barkley's average velocity was 3.41 m/s and his acceleration was 0.325 m/s^{ 2}. Dick Bavetta's average velocity was 3.26 m/s and his acceleration was 0.296 m/s^{2}.

## Sources of Error

- Acceleration wasn't uniform throughout the entire race. The runners had to run up and down the court therefor the acceleration didn't remain constant.
- Another source of error is that both Dick Bavetta and Charles Barkley dove for the finsih line at the end of the race.
- One source of error is the fact that the time used was based on the stop clock on the screen which was not exact.

Olubunmi Fashusi and Shemika White -- 2005

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