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When driving in Kansas in the summer of 2007 with my car on cruise control at the speed limit of 70, I noticed that it didn't take much extra speed to pass a car in a reasonable amount of time. The roads in western Kansas are very straight and lightly traveled.

A. Suppose I want to pass a car that is 150 ft ahead of me and we are both traveling at 70 mi/hr. If he continues at the same speed and I want to be 150 ft ahead of him in 1 minute, what speed should I accelerate to in order to achieve this?

B. Discuss the assumptions you made in order to make this calculation and discuss whether or not they are plausible.

C. If we were both going at 50 mi/hr instead of 70 mi/hr, how would my speed increment change? Discuss this in terms of the equation for average velocity and show how the structure of the equation leads to the result you found. Suppose we had said that I wanted to pass him while he traveled a distance of 1 mile. Would the dependence of my result on his speed change?

D. Suppose we were both going at 25 mi/hr instead of 70 mi/hr in a city? Discuss the mathematical result and the possible shift in the plausibility of our assumptions.

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Page last modified June 24, 2007: K20