Secretariat won the Kentucky Derby with times for successive...

Secretariat won the Kentucky Derby with times for successive quarter-mile segments of $25.2 \mathrm{s}, 24.0 \mathrm{s}, 23.8 \mathrm{s},$ and $23.0 \mathrm{s} .$ (a) Find his average speed during each quarter-mile segment. (b) Assuming that Secretariat's instantaneous speed at the finish line was the same as the average speed during the final quarter mile, find his average acceleration for the entire race. (Horses in the Derby start from rest.)

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Key Concepts

Average Acceleration

Average acceleration is defined as the change in velocity divided by the total time over which the change occurs. This concept is fundamental in kinematics, as it quantifies how quickly an object increases or decreases its speed. When an object starts from rest, average acceleration can be determined by dividing its final speed by the total elapsed time.

Average Speed

Average speed is a measure of the distance traveled divided by the time taken to cover that distance. It is a scalar value that provides a general sense of how fast an object is moving over a specific interval, regardless of changes in speed during that interval.

Instantaneous Speed

Instantaneous speed is the speed of an object at a specific moment in time. It can differ from the average speed over an interval, but under certain assumptions—such as when the instantaneous speed at the end of a segment is taken as representative—it can provide a useful approximation for analyzing motion at particular points.

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