This exercise will be done with groups of 8 or more individuals. Choose one member of the group as the sprinter. Your goal will be to determine the average velocity and average acceleration of the sprinter as a function of time.

Procedure:

Discuss a plan of action with your partners. Stopwatches, measuring tapes, and markers are avaliable. You may request additional equipment from the instructor. Decide how you will calculate the average velocity and acceleration from the measurements that you will make. Your experimental plan should take the following into consideration:

• The effect of the reaction times of both the sprinter and the timers should be minimized.
• You should make a least six measurements over a "reasonable" distance.
• Generally, you want as much data as can be reasonably obtained during the alloted time. However, in consideration of the reproducibility of results, you may need to restrict the number of trials the sprinter has to perform. (A minimum of 3 runs should be performed, but do more if the runner feels up to it.)

When you have finalized your plan, discuss it with the instructor.

Analysis:

1. Determine the average velocity between each pair of cones, then determine the average acceleration between each of your "velocity intervals". Place these calculations in a properly labeled table. Note that you have measurements at equal intervals of space, not time! Before beginning calculations, there will be a group discussion on how to calculate the average velocity and acceleration from the measurements that you have made.
2. Determine an error for each of your velocity and acceleration calculations. Several methods for determining errors, with a specific example for this lab, can be found at Error Analysis. Include those errors in the table.
3. Plot average velocity and average acceleration as a function of distance. Include error bars on the acceleration plot. This will assist you in your discussion.

Report:

Your report should include the following:

• Fully describe your calculations, clearly justifying your choice for time intervals.
• As with all lab reports, show one sample for each unique calculation. (For this lab, there should be one sample for the average velocity calculation and one for acceleration. Include your error in those samples.)
• Estimate the errors involved with your measurements. You should consider reactions times and/or the variability of the data within the runs. When plotting the data, include appropriate error bars for acceleration.
• Discuss any trends you see in the plots. Be sure to justify any conclusions.