he stopping distance d of a car after the brakes are applied varies directly as the square of the speed r. If a car traveling 50 mph can stop in 140 ft, how many feet will it take to same car to stop when it is traveling 80 mph?

Question

he stopping distance d of a car after the brakes are applied varies directly as the square of the speed r.   If a car traveling 50 mph can stop in 140 ft, how many feet will it take to same car to stop when it is traveling 80 mph?

anonymous · Answer

$$d=k s^2$$where d is distance. k is a constant of proportionality and s is the speed.  Using 140 ft at 50 mph$$k=\frac{140}{50^2}=\frac{7}{125} $$At 80 mph$$d= \frac{7}{125} 80^2=\frac{1792}{5}=358.4 \text{ft}$$