The Kentucky Derby is held at the Churchill Downs track inLouisville, Kentucky.

Question

The Kentucky Derby is held at the Churchill Downs track inLouisville, Kentucky. The track is one and one-quarter miles inlength. One of the most famous horses to win this event wasSecretariat. In 1973 he set a Derby record that would be hard tobeat. His average acceleration during the last four quarter-milesof the race was +0.0105 m/s2. His velocity at the startof the final mile (x = +1609 m) was about 16.58 m/s.The acceleration, although small, was very important to hisvictory. To assess its effect, determine the difference between thetime he would have taken to run the final mile at a constantvelocity of +16.58 m/s and the time he actually took. Although thetrack is oval in shape, assume it is straight for the purpose ofthis problem

Explanation / Answer

with a non-constant acceleration vf^2 = vi^2 + 2as vf^2 = 16.58^2 + 2(0.0105)(2011.68 - 1609) vf = 16.83m/s -> ending velocity vf = vi + at 16.83 = 16.58 + (0.0105)(t) t = 23.80 seconds

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