Every time I teach CalcII, I end the semester with a competition (the winner(s) will be dutifully rewarded). It consists in designing your very own word problem. These will be judged in creativity, and in the range of methods it requires, but most importantly, I will only count problems that come together with a CORRECT and COMPLETE solution. Last semester's winner entered and solved the following problem:

A math student notices a Dodge Viper sitting at a stoplight. As the light turns green the driver hammers the gas. The tires spin at 11 rotations per second. The car, however, only accelerate at 4\sqrt{t} ft/sec^2. The student quickly estimates the tire to be 2.5 ft tall and he notices a scuff on the tread of the tire that is initially at (0,2.5).

a). Write equations for the scuff at time t.

b). Suppose the tires grip again when the car speed reaches 85% of the scuff speed. How long is that?

c). When the tire regains traction, how far has the car traveled? The scuff?

d). Write equations for the scuff after the tires have regained traction without restarting the time t, but by matching your initial conditions to the final conditions given by the first part of the motion (namely when the tires were not gripping).