In order to maintain a speed v on a horizontal road a car must supply enough power to overcome air resistance. That required power goes up with increasing speed according to the formula:

P = Power in kW = K × v³

where v is the speed measured in miles/hour and K is a constant of proportionality. Suppose it takes a measured 7.7 kW for a car to overcome air resistance alone at 30.0 mph.

a. What is the value of K in its appropriate units?

b. Using a spreadsheet, prepare a graph of power (kW on the y axis) as a function of speed (mph on the x axis) for speeds from 0 mph to 100 mph.