A Speedboat Ride

After your drive to your lakeside destination, you might want to take a spin in your new speedboat. Speedboats are likely to have speedometers but not odometers. Suppose, given your newfound appreciation of calculus, you would like to somehow apply calculus to your speedboat ride. It turns out that using data from your speedometer and wristwatch, you can determine the distance your boat has travelled. Dimensionally, distance = speed x time or expressed in the style of factor-label analysis  

During a short interval of time At, around a time U, your velocity might be practically constant, that is, u(6) mph. The distance you covered during this time would then be given by u(b)At,. If you start at time ta, the distance you 

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