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

Question

The Kentucky Derby is held at the Churchill Downs track in Louisville, Kentucky. The track is one and one-quarter miles in length. One of the most famous horses to win this event was Secretariat. In 1973 he set a Derby record that would be hard to beat. His average acceleration during the last four quarter-miles of the race was +0.0105 m/s2. His velocity at the start of the final mile (x = +1609 m) was about 16.58 m/s. The acceleration, although small, was very important to his victory. To assess its effect, determine the difference between the time he would have taken to run the final mile at a constant velocity of +16.58 m/s and the time he actually took. Although the track is oval in shape, assume it is straight for the purpose of this problem.
(I think the answer here is also in seconds)

Explanation / Answer

a-without acceleration t=x/v=1609/16.58=97.04 sec b-with a=0.0105 m/sec62 x=vt+at^2/2 --> (0.0105/2)*t^2+16.58*t-1609=0 --> t=77.85 sc (other root is negative, and we dont interested in it)

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