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

Question

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 start of thefinal mile (x=+1609m) was about +16.58m/s. The accelerationalthough small, was very important to his victory. To assess itseffect, determine the difference between the time he would havetaken to run the final mile at a constant velocity of +16.58m/s andthe time he actually took. Although the track is oval in shape,assume it is straight for the purpose of this problem. 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 start of thefinal mile (x=+1609m) was about +16.58m/s. The accelerationalthough small, was very important to his victory. To assess itseffect, determine the difference between the time he would havetaken to run the final mile at a constant velocity of +16.58m/s andthe time he actually took. Although the track is oval in shape,assume it is straight for the purpose of this problem.

Explanation / Answer

Working formulas: With acceleration, S = VT + (1/2)aT^2 W/O acceleration, S = VT where S = 1609 m V = 16.58 T = time to negotiate the last mile a = 0.0105 Substituting values (with acceleration) 1609 = 16.58T + (1/2)(0.0105)T^2 Rearranging the above, 0.00525T^2 + 16.58T - 1609 = 0 Using the quadratic formula, T = 94.233 Without any acceleration, 1609 = 16.58T and solving for T, T = 97.045 sec. Difference in time = 97.045 - 94.233 = 2.812 sec.

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