# Horse Velocity Using Derivatives

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Quarter horses race a distance of 440 yards (a quarter mile) in a straight line. During a race the following observations where made. The top line gives the time in seconds since the race began and the bottom line gives the distance (in yards) the horse has traveled from the starting line.

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1. How fast is the horse running halfway through the race?

2. Find a formula for the velocity of the horse.

3. The horse will win a bonus if the time for the race is less than 22 seconds. Decide whether you think the horse will win the bonus. Explain your reasons.

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##### Solution Summary

The expert examines horse velocity using derivatives. How fast the horse is running halfway through the race is given.

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Hi, this is a great question. Start out by making your own plot of the data. I did not include a plot, because I think it is beneficial for you to do this step. If you plot the given data (distance vs. time), you will see that it is pretty much a line. The general rule is that if a distance vs. time plot is a straight positive sloping line, then the corresponding velocity is positive and constant. Therefore, the velocity in the middle can be calculated by taking the difference of two of the distances and dividing it by the corresponding time points in ...

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