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 has never been broken. 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.
2007-09-12 16:38:57 · 1 answers · asked by lonelygirlinhell 1 in Science & Mathematics ➔ Physics
x=xo+vo*t+at^2/2
Here, t is time after he ran a mile, so xo=0.
so x=402 m
vo=16.58 m/sec
a=0.0105.
We can solve this quadratic for t, discarding the extraneous root.
Then we can solve 402= 16.58*t0, where t0 is the hypothetical time at constant velocity. The difference between t0 and t is your answer.
2007-09-12 16:51:36 · answer #1 · answered by cattbarf 7 · 0⤊ 0⤋