Automobile skid marks The speed Vat which an automobile was traveling before the brakes were applied can sometimes be estimated from the length L of the skid marks. Assume that V is directly proportional to the square root of L. (a) Express V as a function of L by means of a formula that involves a constant of proportionality k. (b) For a certain automobile on a dry surface, L = 50 ft when V = 35 mi/hr. Find the value of k in part (a). (c) Estimate the initial speed of the automobile in part (b) if the skid marks are 150 feet long.

Power of a wind rotor The power P generated by a wind rotor is directly proportional to the product of the square of the area A swept out by the blades and the third power of the wind velocity v. Suppose the diameter of the circular area swept out by the blades is 10 feet, and P = 3000 watts when v = 20 mi/hr. Find the power generated when the wind velocity is 30 mi/hr.

The amount of time it takes to drive somewhere is inversely proportional to the speed at which you drive. The time of a trip is 3 hours when you drive at 60 km/h. a) Determine the equation for the function t(v), which relating the time of the trip ("t", in hours) to the speed (v, in km/h). b) Find the time it would take to complete the above trip if you drove at 90 km/h. c) What speed should you drive at to complete the trip in 75 minutes? 2.

The stopping distance d (in feet) for a car traveling v mph when the driver has a reaction time of t is given by d = 1.5tv + 0.06v². A car is traveling 70 mph. If the driver's reaction time is 0.5 sec, what is the stopping distance? ft