Question

Instructor Math 112 Section: Directions: Show all work, and answer each question that is asked. Explanations should be given in complete sentences. All graphs should be drawn accurately on this sheet, and be fully labeled 1. The stopping distance of a car, d, as a function of its speed, v, is given by the function d kv2 where k is a constant that is dependent on the specific car and conditions of the road. Suppose a certain car traveling 50 mph requires 112.5 feet to stop. Find the constant k, and use that information to approximate the stopping distance for this car traveling at 80 mph. e問勿

Answer 1

d = k v^2 - (1) speed of car v_1 = 50 mph d_1 = required distance to stop = 112.5 feet because v_1 = 50 Miles/hour because 1 miles = 5280 feet so v_1 = 50 times 5280 feet/hour now, putting the values of v_1 and d_1 in eq^n (1) (in feet) 112.5(feet) = k middot (50 times 5280 f/h)^2 k = 112.5/50 times 5280 k = 0.0004261 hour^2/feet now as we know that d proportionalto v^2 (for the same car) when, speed 50 mph rightarrow distance 112.5 feet the speed 80 mph rightarrow ? (50/80)^2 = 112.5/d d = 112.5 times 2.56 = 200 feet so, at 20 mph the car will take 200 feet to stop.